Details

Time bar (total: 7.3s)

analyze37.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%25%75%0
0%25%75%1
12.5%12.5%75%2
12.5%12.5%75%3
18.7%6.2%75%4
21.8%3.1%75%5
23.4%1.6%75%6
23.4%1.6%75%7
24.2%0.8%75%8
24.2%0.8%75%9
24.6%0.4%75%10
24.6%0.4%75%11
24.8%0.2%75%12
24.8%0.2%75%13
24.9%0.1%75%14
Compiler

Compiled 17 to 12 computations (29.4% saved)

sample54.0ms (0.7%)

Algorithm
intervals
Results
17.0ms57×body1024valid
13.0ms165×body128valid
5.0ms256×pre128true
4.0ms21×body512valid
2.0ms13×body256valid
Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify13.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-/r/_binary64 associate-/l*_binary64
1-exp_binary64 +-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
11717
22117
32417
42517
52417

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.2b
Counts
1 → 1
Alt Table
StatusErrorProgram
0.2b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
Compiler

Compiled 26 to 18 computations (30.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(sin.f64 v)
0.0b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
0.1b
(*.f64 e (cos.f64 v))
0.1b
(*.f64 e (sin.f64 v))

rewrite95.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
14×add-sqr-sqrt_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64
pow1_binary64
associate-*l*_binary64 associate-*r*_binary64
Counts
4 → 66
Calls

4 calls:

6.0ms
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
4.0ms
(*.f64 e (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
2.0ms
(sin.f64 v)
Compiler

Compiled 1123 to 406 computations (63.8% saved)

series114.0ms (1.6%)

Error
0.2b
Counts
4 → 33
Calls

4 calls:

45.0ms
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
19.0ms
(*.f64 e (sin.f64 v))
16.0ms
(*.f64 e (cos.f64 v))
8.0ms
(sin.f64 v)
Compiler

Compiled 1511 to 1032 computations (31.7% saved)

simplify109.0ms (1.5%)

Algorithm
egg-herbie
Rules
526×associate-/r*_binary64
400×associate-*l/_binary64
303×associate-/r/_binary64
298×cancel-sign-sub-inv_binary64
290×associate-/l/_binary64
Counts
99 → 45
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01941756
15241596
220011571
348781571
449931571
549541571

prune60.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New39645
Fresh000
Picked011
Done000
Total39746
Error
0.0b
Counts
46 → 7
Alt Table
StatusErrorProgram
0.2b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
22.6b
(*.f64 (sqrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))) (sqrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))))
0.2b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
0.8b
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))
0.4b
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
1.1b
(/.f64 (*.f64 (*.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
Compiler

Compiled 1170 to 643 computations (45% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(sin.f64 v)
0.1b
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
0.1b
(*.f64 e (cos.f64 v))
0.2b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))

rewrite211.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
84×times-frac_binary64
58×add-sqr-sqrt_binary64
56×add-cube-cbrt_binary64 *-un-lft-identity_binary64
16×associate-/r*_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
Counts
4 → 124
Calls

4 calls:

9.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
7.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
5.0ms
(*.f64 e (cos.f64 v))
1.0ms
(sin.f64 v)
Compiler

Compiled 2748 to 1134 computations (58.7% saved)

series137.0ms (1.9%)

Error
0.0b
Counts
4 → 36
Calls

4 calls:

45.0ms
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
37.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
16.0ms
(*.f64 e (cos.f64 v))
7.0ms
(sin.f64 v)
Compiler

Compiled 1634 to 1106 computations (32.3% saved)

simplify157.0ms (2.2%)

Algorithm
egg-herbie
Rules
690×associate-/r/_binary64
379×cancel-sign-sub-inv_binary64
190×sub-neg_binary64
165×associate-*r*_binary64
164×associate-/l*_binary64
Counts
160 → 121
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03074239
17714008
228003968
346223968
449683968

prune308.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1165121
Fresh325
Picked011
Done011
Total1199128
Error
0.0b
Counts
128 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))))
0.9b
(/.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (cbrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))))) e) (/.f64 (cbrt.f64 (+.f64 (*.f64 e (cos.f64 v)) 1)) (cbrt.f64 (sin.f64 v))))
9.1b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (cbrt.f64 (pow.f64 (sin.f64 v) 3))))
0.2b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (cbrt.f64 e) (/.f64 (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (cbrt.f64 (sin.f64 v)))))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))))
0.2b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
0.9b
(/.f64 e (/.f64 (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))))
0.8b
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))
Compiler

Compiled 2924 to 1344 computations (54% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
0.1b
(*.f64 e (cos.f64 v))
0.2b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))))
0.3b
(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

rewrite449.0ms (6.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
294×times-frac_binary64
196×add-sqr-sqrt_binary64
162×add-cube-cbrt_binary64 *-un-lft-identity_binary64
93×sqrt-prod_binary64
86×associate-*r*_binary64
Counts
4 → 274
Calls

4 calls:

30.0ms
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))))
11.0ms
(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
5.0ms
(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
4.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 6991 to 2673 computations (61.8% saved)

series200.0ms (2.8%)

Error
0.0b
Counts
4 → 39
Calls

4 calls:

54.0ms
(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
48.0ms
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))))
37.0ms
(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
19.0ms
(*.f64 e (cos.f64 v))
Compiler

Compiled 2455 to 1649 computations (32.8% saved)

simplify249.0ms (3.4%)

Algorithm
egg-herbie
Rules
374×associate-*l*_binary64
348×associate-*r*_binary64
293×*-commutative_binary64
289×associate-/l*_binary64
239×associate-*l/_binary64
Counts
313 → 271
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04639909
111949530
246409454
349789454

prune292.0ms (4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2701271
Fresh156
Picked011
Done022
Total2719280
Error
0b
Counts
280 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))))
0.9b
(/.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (cbrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))))) e) (/.f64 (cbrt.f64 (+.f64 (*.f64 e (cos.f64 v)) 1)) (cbrt.f64 (sin.f64 v))))
0.5b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))))
9.1b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (cbrt.f64 (pow.f64 (sin.f64 v) 3))))
0.2b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (cbrt.f64 e) (/.f64 (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (cbrt.f64 (sin.f64 v)))))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))))
0.2b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
0.8b
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))
Compiler

Compiled 5901 to 2445 computations (58.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))))
0.3b
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))
0.3b
(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
0.4b
(/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))))

rewrite395.0ms (5.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
192×times-frac_binary64
160×sqrt-prod_binary64
124×add-sqr-sqrt_binary64
96×add-cube-cbrt_binary64 *-un-lft-identity_binary64
77×associate-*r*_binary64
Counts
4 → 245
Calls

4 calls:

35.0ms
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))))
17.0ms
(/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))))
10.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))
7.0ms
(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
Compiler

Compiled 6887 to 2178 computations (68.4% saved)

series264.0ms (3.6%)

Error
0b
Counts
4 → 41
Calls

4 calls:

69.0ms
(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))
53.0ms
(/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))))
47.0ms
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))))
38.0ms
(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
Compiler

Compiled 3088 to 2161 computations (30% saved)

simplify249.0ms (3.4%)

Algorithm
egg-herbie
Rules
495×associate-*r*_binary64
449×associate-*l*_binary64
272×associate-/l*_binary64
224×associate-*r/_binary64
182×times-frac_binary64
Counts
286 → 194
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045310942
112279588
247419568
349739568

prune205.0ms (2.8%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New1931194
Fresh145
Picked011
Done033
Total1949203
Error
0b
Counts
203 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))))
0.9b
(/.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (*.f64 (cbrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (cbrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))))) e) (/.f64 (cbrt.f64 (+.f64 (*.f64 e (cos.f64 v)) 1)) (cbrt.f64 (sin.f64 v))))
0.6b
(*.f64 (*.f64 (sqrt.f64 e) (sqrt.f64 (fabs.f64 (cbrt.f64 e)))) (/.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 e))) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))))
0.5b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 (sqrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))))))
0.2b
(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (cbrt.f64 e) (/.f64 (sqrt.f64 (+.f64 1 (*.f64 e (cos.f64 v)))) (cbrt.f64 (sin.f64 v)))))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (+.f64 (*.f64 e (cos.f64 v)) 1))))
0.2b
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 1 (*.f64 e (cos.f64 v))))
0.8b
(/.f64 1 (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (*.f64 e (sin.f64 v))))
Compiler

Compiled 4101 to 1738 computations (57.6% saved)

regimes1.6s (22.2%)

Accuracy

Total 0.1b remaining (84.4%)

Threshold costs 0.1b (84.4%)

Compiler

Compiled 28191 to 16826 computations (40.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64 *-lft-identity_binary64 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01117
11717
21617

end1.0ms (0%)

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.0s (27.6%)

Algorithm
intervals
Results
617.0ms2011×body1024valid
331.0ms4465×body128valid
219.0ms1018×body512valid
173.0ms8000×pre128true
79.0ms503×body256valid
2.0msbody2048valid
Compiler

Compiled 257 to 156 computations (39.3% saved)

Profiling

Loading profile data...