Details

Time bar (total: 9.5s)

analyze2.1s (22.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
1.6%98.3%0.1%11
1.6%98.3%0.1%12
2.3%97.5%0.1%13
3.5%96.3%0.1%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample4.1s (42.6%)

Results
2.5s3589×body1024valid
603.0ms1428×body512valid
420.0ms2444×body128valid
306.0ms205×body2048valid
173.0ms590×body256valid
4.0msbody8192exit
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-/l*_binary64
associate-/r/_binary64
+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11314
21714
32014
42114
52114

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
12.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
12.3b
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
Compiler

Compiled 45 to 27 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 r (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.4b
(cos.f64 (+.f64 a b))

series62.0ms (0.7%)

Counts
3 → 68
Calls

3 calls:

50.0ms
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
7.0ms
(*.f64 r (sin.f64 b))
4.0ms
(cos.f64 (+.f64 a b))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 53
Calls

3 calls:

4.0ms
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms
(cos.f64 (+.f64 a b))
3.0ms
(*.f64 r (sin.f64 b))

simplify66.0ms (0.7%)

Algorithm
egg-herbie
Rules
558×fma-def_binary64
517×associate-/r*_binary64
394×associate-*l/_binary64
321×associate-/l/_binary64
308×associate-/r/_binary64
Counts
121 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02002011
15251879
220031831
350441831

prune129.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1159124
Fresh000
Picked101
Done000
Total1169125
Error
0.1b
Counts
125 → 9
Alt Table
StatusErrorProgram
12.4b
(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
12.4b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
12.4b
(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b)))))
12.5b
(/.f64 (*.f64 r (sin.f64 b)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 3)))
12.3b
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
27.4b
(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))
12.5b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 a b)))))
12.4b
(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
Compiler

Compiled 2539 to 896 computations (64.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
0.1b
(*.f64 r (sin.f64 b))
0.2b
(*.f64 (sin.f64 a) (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series147.0ms (1.5%)

Counts
3 → 64
Calls

3 calls:

119.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
17.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
10.0ms
(*.f64 (sin.f64 a) (sin.f64 b))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 66
Calls

3 calls:

8.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
4.0ms
(*.f64 (sin.f64 a) (sin.f64 b))

simplify137.0ms (1.4%)

Algorithm
egg-herbie
Rules
824×fma-def_binary64
381×fma-neg_binary64
329×cancel-sign-sub-inv_binary64
204×associate-*r*_binary64
204×distribute-rgt-neg-in_binary64
Counts
130 → 156
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02523500
16913279
225843054
345783049
449963049
549233049

prune259.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New18410194
Fresh718
Picked101
Done000
Total19211203
Error
0.0b
Counts
203 → 11
Alt Table
StatusErrorProgram
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.3b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.5b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (/.f64 (exp.f64 (*.f64 (cos.f64 a) (cos.f64 b))) (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))
21.5b
(*.f64 (/.f64 r (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.4b
(*.f64 (/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b))) (*.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.5b
(/.f64 (*.f64 r (sin.f64 b)) (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (sin.f64 b) (*.f64 (sin.f64 a) (fma.f64 (sin.f64 b) (sin.f64 a) (*.f64 (cos.f64 a) (cos.f64 b)))) (*.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)))))
1.1b
(/.f64 (*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (cbrt.f64 (sin.f64 b))) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1))))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))))
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
12.4b
(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
0.4b
(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))
Compiler

Compiled 5563 to 1559 computations (72% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))
0.1b
(*.f64 r (sin.f64 b))
0.2b
(*.f64 (sin.f64 a) (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))

series136.0ms (1.4%)

Counts
2 → 60
Calls

2 calls:

120.0ms
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
16.0ms
(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 33
Calls

2 calls:

4.0ms
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
0.0ms
(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

simplify72.0ms (0.8%)

Algorithm
egg-herbie
Rules
656×associate-*l*_binary64
468×fma-def_binary64
441×associate-/r*_binary64
304×associate-*l/_binary64
267×associate-/l/_binary64
Counts
93 → 88
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01702771
14512573
216502534
352102534

prune214.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1685173
Fresh3710
Picked101
Done000
Total17212184
Error
0.0b
Counts
184 → 12
Alt Table
StatusErrorProgram
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.3b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.5b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (/.f64 (exp.f64 (*.f64 (cos.f64 a) (cos.f64 b))) (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
21.5b
(*.f64 (/.f64 r (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.4b
(*.f64 (/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b))) (*.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.4b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
1.1b
(/.f64 (*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (cbrt.f64 (sin.f64 b))) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.3b
(/.f64 r (/.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) (sin.f64 b)))
48.1b
(/.f64 (*.f64 (*.f64 (sqrt.f64 r) (sqrt.f64 (sin.f64 b))) (*.f64 (sqrt.f64 r) (sqrt.f64 (sin.f64 b)))) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
0.4b
(/.f64 1 (/.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) (*.f64 r (sin.f64 b))))
12.4b
(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
Compiler

Compiled 4938 to 1406 computations (71.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))
0.1b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b
(*.f64 (sin.f64 b) (sin.f64 a))
0.2b
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

series215.0ms (2.3%)

Counts
4 → 76
Calls

4 calls:

118.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
67.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
19.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))
11.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

rewrite35.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
20×associate-*r*_binary64
19×times-frac_binary64
Counts
4 → 110
Calls

4 calls:

9.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
8.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))
7.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
4.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

simplify181.0ms (1.9%)

Algorithm
egg-herbie
Rules
367×fma-neg_binary64
327×cancel-sign-sub-inv_binary64
298×associate-*r*_binary64
265×associate-*l*_binary64
203×associate-/l*_binary64
Counts
186 → 253
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03365467
18765149
233354803
345024797
449844797
549334797

prune329.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2503253
Fresh4711
Picked101
Done000
Total25510265
Error
0.0b
Counts
265 → 10
Alt Table
StatusErrorProgram
21.5b
(*.f64 (/.f64 r (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.4b
(*.f64 r (*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (*.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2)))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
0.4b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
1.1b
(/.f64 (*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (cbrt.f64 (sin.f64 b))) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.3b
(/.f64 r (/.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) (sin.f64 b)))
0.4b
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
12.4b
(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
0.3b
(*.f64 r (/.f64 1 (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a))))
Compiler

Compiled 7420 to 1837 computations (75.2% saved)

regimes1.1s (11.4%)

Accuracy

Total 0.3b remaining (82.5%)

Threshold costs 0.3b (82.5%)

Counts
236 → 1
Compiler

Compiled 23488 to 13564 computations (42.3% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01326
12326
23126
33626
43826
53826

end168.0ms (1.8%)

Compiler

Compiled 308 to 169 computations (45.1% saved)

Profiling

Loading profile data...