Details

Time bar (total: 10.6s)

analyze2.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 27 to 22 computations (18.5% saved)

sample3.6s (33.4%)

Results
1.4s1871×body1024valid
925.0ms4747×body128valid
571.0ms1038×body512valid
214.0ms46×body4096valid
174.0ms452×body256valid
137.0ms102×body2048valid
Compiler

Compiled 80 to 65 computations (18.8% saved)

simplify39.0ms (0.4%)

Algorithm
egg-herbie
Rules
387×unsub-neg_binary64
380×neg-sub0_binary64
373×neg-mul-1_binary64
358×*-commutative_binary64
328×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01737
13737
28437
322437
480337
5206137
6386137
7507637

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
31.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
31.3b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
Compiler

Compiled 101 to 78 computations (22.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(-.f64 (pow.f64 b 2) (pow.f64 a 2))
8.4b
(*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
26.8b
(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
27.2b
(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series71.0ms (0.7%)

Counts
4 → 66
Calls

4 calls:

56.0ms
(*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
8.0ms
(-.f64 (pow.f64 b 2) (pow.f64 a 2))
3.0ms
(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
3.0ms
(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

rewrite32.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
64×prod-diff_binary64
64×unpow-prod-down_binary64
57×add-sqr-sqrt_binary64
45×*-un-lft-identity_binary64
41×add-cube-cbrt_binary64
Counts
4 → 151
Calls

4 calls:

10.0ms
(*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
8.0ms
(-.f64 (pow.f64 b 2) (pow.f64 a 2))
1.0ms
(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
1.0ms
(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

simplify175.0ms (1.7%)

Algorithm
egg-herbie
Rules
580×cancel-sign-sub-inv_binary64
482×fma-neg_binary64
457×unswap-sqr_binary64
363×associate-*r*_binary64
310×associate-*l*_binary64
Counts
217 → 222
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03388304
17014859
225063469
345943463
449813463
548713463

prune626.0ms (5.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New20517222
Fresh000
Picked101
Done000
Total20617223
Error
21.4b
Counts
223 → 17
Alt Table
StatusErrorProgram
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
44.6b
(*.f64 (-.f64 (+.f64 (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 a 2)))) (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 b 2))))) (+.f64 (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 a 2)))) (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 b 2)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.2b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
46.0b
(*.f64 (*.f64 (*.f64 2 (*.f64 (+.f64 b (pow.f64 (sqrt.f64 a) 2)) (-.f64 b (pow.f64 (sqrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
57.3b
(*.f64 (*.f64 (*.f64 2 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 a 6)) (fma.f64 (*.f64 a a) (fma.f64 a a (*.f64 b b)) (pow.f64 b 4)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.4b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
46.1b
(*.f64 (exp.f64 (log.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (*.f64 2 (-.f64 (*.f64 b b) (*.f64 a a)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
44.1b
(*.f64 (*.f64 (*.f64 2 (expm1.f64 (log1p.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2))))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
33.9b
(*.f64 (*.f64 angle (*.f64 1/90 (*.f64 (PI.f64) (-.f64 (*.f64 b b) (*.f64 a a))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
42.9b
(*.f64 (*.f64 2 (*.f64 (pow.f64 b 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.1b
(*.f64 (*.f64 -2 (*.f64 (pow.f64 a 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
35.2b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (*.f64 (sqrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (sqrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
34.4b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (fma.f64 angle (*.f64 (PI.f64) 1/180) (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 angle 3) -1/34992000)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
32.9b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1)
57.9b
(*.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (log.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
Compiler

Compiled 9734 to 6948 computations (28.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(-.f64 (pow.f64 b 2) (pow.f64 a 2))
8.4b
(*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
26.8b
(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
27.0b
(cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))

series4.0ms (0%)

Counts
1 → 4
Calls

1 calls:

3.0ms
(cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 9
Calls

1 calls:

1.0ms
(cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))

simplify63.0ms (0.6%)

Algorithm
egg-herbie
Rules
861×distribute-rgt-neg-in_binary64
699×distribute-lft-neg-in_binary64
488×fma-def_binary64
475×cancel-sign-sub-inv_binary64
369×*-commutative_binary64
Counts
13 → 17
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
040238
194217
2246213
3973211
42721205
54427205
64978205

prune452.0ms (4.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New2174221
Fresh21416
Picked101
Done000
Total22018238
Error
21.4b
Counts
238 → 18
Alt Table
StatusErrorProgram
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
44.6b
(*.f64 (-.f64 (+.f64 (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 a 2)))) (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 b 2))))) (+.f64 (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 a 2)))) (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 b 2)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.2b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
46.0b
(*.f64 (*.f64 (*.f64 2 (*.f64 (+.f64 b (pow.f64 (sqrt.f64 a) 2)) (-.f64 b (pow.f64 (sqrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
42.9b
(*.f64 (*.f64 2 (*.f64 (pow.f64 b 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
34.1b
(*.f64 (*.f64 angle (*.f64 1/90 (*.f64 (PI.f64) (-.f64 (*.f64 b b) (*.f64 a a))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.5b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
57.3b
(*.f64 (*.f64 (*.f64 2 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 a 6)) (fma.f64 (*.f64 a a) (fma.f64 a a (*.f64 b b)) (pow.f64 b 4)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
32.9b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1)
45.7b
(*.f64 (exp.f64 (log.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
57.9b
(*.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (log.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.6b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
44.1b
(*.f64 (*.f64 (*.f64 2 (expm1.f64 (log1p.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2))))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.1b
(*.f64 (*.f64 -2 (*.f64 (pow.f64 a 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
35.2b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (*.f64 (sqrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (sqrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
34.4b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (fma.f64 angle (*.f64 (PI.f64) 1/180) (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 angle 3) -1/34992000)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
Compiler

Compiled 9776 to 6762 computations (30.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))
8.4b
(*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
26.8b
(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
27.2b
(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series92.0ms (0.9%)

Counts
2 → 60
Calls

2 calls:

71.0ms
(*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
20.0ms
(+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
fma-def_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
Counts
2 → 44
Calls

2 calls:

8.0ms
(*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
4.0ms
(+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))

simplify115.0ms (1.1%)

Algorithm
egg-herbie
Rules
867×fma-def_binary64
534×fma-neg_binary64
420×cancel-sign-sub-inv_binary64
265×neg-mul-1_binary64
250×associate-*r*_binary64
Counts
104 → 86
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01563310
14642307
218852079
342712071
449992071
549732071

prune266.0ms (2.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New1157122
Fresh21517
Picked101
Done000
Total11822140
Error
21.4b
Counts
140 → 22
Alt Table
StatusErrorProgram
31.1b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
44.1b
(*.f64 (*.f64 (*.f64 2 (expm1.f64 (log1p.f64 (-.f64 (pow.f64 b 2) (pow.f64 a 2))))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
44.6b
(*.f64 (-.f64 (+.f64 (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 a 2)))) (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 b 2))))) (+.f64 (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 a 2)))) (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 b 2)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.2b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
46.0b
(*.f64 (*.f64 (*.f64 2 (*.f64 (+.f64 b (pow.f64 (sqrt.f64 a) 2)) (-.f64 b (pow.f64 (sqrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
42.9b
(*.f64 (*.f64 2 (*.f64 (pow.f64 b 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
34.1b
(*.f64 (*.f64 angle (*.f64 1/90 (*.f64 (PI.f64) (-.f64 (*.f64 b b) (*.f64 a a))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
58.3b
(*.f64 (/.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (*.f64 2 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 a a) 3)))) (+.f64 (*.f64 (pow.f64 b 2) (pow.f64 b 2)) (-.f64 (*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2))) (*.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.1b
(*.f64 (*.f64 -2 (*.f64 (pow.f64 a 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
33.0b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1)
32.9b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1)
45.7b
(*.f64 (exp.f64 (log.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
57.9b
(*.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (log.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.6b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.5b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (log.f64 (exp.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
34.3b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (*.f64 1/180 (*.f64 angle (PI.f64)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
34.4b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (fma.f64 angle (*.f64 (PI.f64) 1/180) (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 angle 3) -1/34992000)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
57.3b
(*.f64 (*.f64 (*.f64 2 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 a 6)) (fma.f64 (*.f64 a a) (fma.f64 a a (*.f64 b b)) (pow.f64 b 4)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
31.6b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
Compiler

Compiled 6757 to 4515 computations (33.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))
8.3b
(*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
26.6b
(sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))
27.2b
(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series76.0ms (0.7%)

Counts
2 → 40
Calls

2 calls:

72.0ms
(*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
4.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*r*_binary64
cbrt-unprod_binary64
Counts
2 → 31
Calls

2 calls:

7.0ms
(*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
2.0ms
(sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))

simplify88.0ms (0.8%)

Algorithm
egg-herbie
Rules
460×cancel-sign-sub-inv_binary64
443×fma-neg_binary64
438×distribute-rgt-in_binary64
275×neg-mul-1_binary64
269×unswap-sqr_binary64
Counts
71 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01542862
14682051
219481913
344401906
451041906

prune291.0ms (2.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New1164120
Fresh12021
Picked101
Done000
Total11824142
Error
21.4b
Counts
142 → 24
Alt Table
StatusErrorProgram
31.1b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
34.3b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (*.f64 1/180 (*.f64 angle (PI.f64)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
44.6b
(*.f64 (-.f64 (+.f64 (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 a 2)))) (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 b 2))))) (+.f64 (*.f64 1/90 (*.f64 angle (*.f64 (PI.f64) (pow.f64 a 2)))) (*.f64 1/17496000 (*.f64 (pow.f64 angle 3) (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 b 2)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.2b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
46.0b
(*.f64 (*.f64 (*.f64 2 (*.f64 (+.f64 b (pow.f64 (sqrt.f64 a) 2)) (-.f64 b (pow.f64 (sqrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
42.9b
(*.f64 (*.f64 2 (*.f64 (pow.f64 b 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
34.1b
(*.f64 (*.f64 angle (*.f64 1/90 (*.f64 (PI.f64) (-.f64 (*.f64 b b) (*.f64 a a))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
44.0b
(*.f64 (*.f64 (*.f64 2 (expm1.f64 (log1p.f64 (-.f64 (*.f64 b b) (*.f64 a a))))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
41.1b
(*.f64 (*.f64 -2 (*.f64 (pow.f64 a 2) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
58.3b
(*.f64 (/.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) (*.f64 2 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 a a) 3)))) (+.f64 (*.f64 (pow.f64 b 2) (pow.f64 b 2)) (-.f64 (*.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2))) (*.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
33.0b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1)
34.0b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) 1)
32.9b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1)
45.7b
(*.f64 (exp.f64 (log.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.5b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
57.9b
(*.f64 (exp.f64 (+.f64 (log.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))) (log.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.6b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.7b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 1/180 (*.f64 angle (PI.f64))))) (cos.f64 (*.f64 1/180 (*.f64 angle (PI.f64)))))
31.5b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (log.f64 (exp.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
34.4b
(*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (fma.f64 angle (*.f64 (PI.f64) 1/180) (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 angle 3) -1/34992000)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
57.3b
(*.f64 (*.f64 (*.f64 2 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 a 6)) (fma.f64 (*.f64 a a) (fma.f64 a a (*.f64 b b)) (pow.f64 b 4)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
31.5b
(*.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
31.6b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) (cbrt.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cbrt.f64 (*.f64 (*.f64 2 (+.f64 (pow.f64 b 2) (*.f64 (neg.f64 (pow.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) 2)) (pow.f64 (cbrt.f64 a) 2)))) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) (cos.f64 (*.f64 (PI.f64) (/.f64 angle 180))))
Compiler

Compiled 5931 to 3768 computations (36.5% saved)

regimes3.8s (36%)

Accuracy

Total 9.2b remaining (32.4%)

Threshold costs 0b (0%)

Counts
189 → 4
Compiler

Compiled 85677 to 64726 computations (24.5% saved)

bsearch138.0ms (1.3%)

Steps
ItersRangePoint
7
2.0955084048413263e+241
5.102002757441132e+242
2.5050279053317988e+241
1
1.4182383285205369e+75
1.5283348926172071e+75
1.4457624695447043e+75
10
-2.192978860643054e+163
-2.2403407736569772e+150
-9.389831201206458e+153
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
20×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
051172
174172
282172
386172
488172
588172

end605.0ms (5.7%)

Compiler

Compiled 1156 to 861 computations (25.5% saved)

Profiling

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