Details

analyze2.4s (14.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5136	473
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample56.0ms (0.4%)

Algorithm

1×

intervals

Results

31.0ms	251×	body	128	valid
2.0ms	18×	body	128	invalid
1.0ms	3×	body	1024	invalid
1.0ms	2×	body	1024	valid
1.0ms	3×	body	512	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

12.9b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
30.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite177.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

12.9b

Rules

20×	`*-un-lft-identity_binary64_760`
16×	`add-sqr-sqrt_binary64_782`
12×	`add-log-exp_binary64_799`
9×	`add-cube-cbrt_binary64_795`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`unpow-prod-down_binary64_839` `exp-prod_binary64_812`
5×	`pow1_binary64_821` `add-exp-log_binary64_798` `exp-sum_binary64_806`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `distribute-lft-out_binary64_711` `rem-exp-log_binary64_800`
2×	`sub-neg_binary64_753` `sum-log_binary64_851` `diff-log_binary64_852`
1×	`cos-diff_binary64_897` `times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `exp-diff_binary64_808`

Counts

4 → 67

Calls

4 calls:

22.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 2607 to 1322 computations (49.3% saved)

series1.5s (9.2%)

Error

1.0b

Counts

4 → 90

Calls

4 calls:

588.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
296.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
273.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
149.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 9292 to 6155 computations (33.8% saved)

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5035	3834

prune242.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	6	158

Error

1.1b

Counts

158 → 6

Compiler

Compiled 5721 to 2695 computations (52.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite152.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

22×	`*-un-lft-identity_binary64_760`
21×	`add-sqr-sqrt_binary64_782`
14×	`add-log-exp_binary64_799`
9×	`add-cube-cbrt_binary64_795`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`unpow-prod-down_binary64_839` `exp-prod_binary64_812`
5×	`difference-of-squares_binary64_729` `pow1_binary64_821` `add-exp-log_binary64_798` `exp-sum_binary64_806`
4×	`distribute-lft-out--_binary64_712` `add-cbrt-cube_binary64_796`
3×	`pow-unpow_binary64_837` `distribute-lft-out_binary64_711` `diff-log_binary64_852` `rem-exp-log_binary64_800`
2×	`times-frac_binary64_766` `sum-log_binary64_851` `sub-neg_binary64_753`
1×	`pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `exp-diff_binary64_808` `flip3--_binary64_764` `flip--_binary64_735`

Counts

4 → 72

Calls

4 calls:

18.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
14.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 2149 to 1096 computations (49% saved)

series1.4s (8.7%)

Error

1.1b

Counts

4 → 93

Calls

4 calls:

582.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
267.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
259.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
148.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

Compiler

Compiled 7266 to 4993 computations (31.3% saved)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5082	3651

prune198.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	165	6	171

Error

1.1b

Counts

171 → 6

Compiler

Compiled 4534 to 2085 computations (54% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 m (sin.f64 (-.f64 (.f64 1/2 (*.f64 K n)) M)))
6.9b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
22.0b	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
22.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

rewrite259.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

17×	`add-sqr-sqrt_binary64_782`
16×	`cancel-sign-sub-inv_binary64_726`
15×	`*-un-lft-identity_binary64_760`
13×	`add-cube-cbrt_binary64_795`
12×	`sin-sum_binary64_893`
11×	`associate-r_binary64_700`
8×	`pow1_binary64_821` `add-cbrt-cube_binary64_796`
7×	`add-exp-log_binary64_798`
6×	`associate-l_binary64_701`
5×	`sub-neg_binary64_753` `exp-sum_binary64_806`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709`
3×	`exp-diff_binary64_808`
2×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `flip3--_binary64_764` `frac-times_binary64_770` `flip--_binary64_735` `unswap-sqr_binary64_728` `associate-l/_binary64_703` `-commutative_binary64_691`
1×	`cos-diff_binary64_897` `sin-diff_binary64_896` `associate-*r/_binary64_702` `distribute-lft-out_binary64_711`

Counts

4 → 78

Calls

4 calls:

26.0ms	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
10.0ms	(.f64 m (sin.f64 (-.f64 (.f64 1/2 (*.f64 K n)) M)))
7.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
7.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

Compiler

Compiled 4629 to 2521 computations (45.5% saved)

series1.9s (11.9%)

Error

1.1b

Counts

4 → 58

Calls

4 calls:

1.4s	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
204.0ms	(.f64 m (sin.f64 (-.f64 (.f64 1/2 (*.f64 K n)) M)))
85.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
76.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

Compiler

Compiled 10779 to 6775 computations (37.1% saved)

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5046	6847

prune353.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	136	6	142

Error

1.1b

Counts

142 → 6

Compiler

Compiled 8015 to 4085 computations (49% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 m)
6.9b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (cbrt.f64 m)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
22.0b	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
22.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

rewrite226.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

12×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795` `cancel-sign-sub-inv_binary64_726`
8×	`associate-r_binary64_700`
6×	`pow1_binary64_821` `add-cbrt-cube_binary64_796`
5×	`add-exp-log_binary64_798` `exp-sum_binary64_806`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `sin-sum_binary64_893`
3×	`sub-neg_binary64_753` `exp-diff_binary64_808` `associate-l_binary64_701` `cbrt-prod_binary64_791`
2×	`flip3--_binary64_764` `frac-times_binary64_770` `flip--_binary64_735` `associate-*l/_binary64_703`
1×	`cos-diff_binary64_897` `sin-diff_binary64_896` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `associate-r/_binary64_702` `distribute-lft-out_binary64_711` `-commutative_binary64_691` `pow1/3_binary64_842`

Counts

4 → 63

Calls

4 calls:

27.0ms	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (cbrt.f64 m)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
9.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
7.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
1.0ms	(cbrt.f64 m)

Compiler

Compiled 4317 to 2139 computations (50.5% saved)

series1.9s (11.7%)

Error

1.1b

Counts

4 → 47

Calls

4 calls:

1.5s	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (.f64 1/2 (.f64 K (.f64 (.f64 (cbrt.f64 m) (cbrt.f64 m)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M)) (cbrt.f64 m)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
91.0ms	(sin.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
81.0ms	(cbrt.f64 m)
75.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

Compiler

Compiled 9967 to 6105 computations (38.7% saved)

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5331	6052

prune264.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	110	6	116

Error

1.1b

Counts

116 → 6

Compiler

Compiled 6984 to 3340 computations (52.2% saved)

regimes1.1s (6.7%)

Accuracy

Total 0.2b remaining (15.5%)

Threshold costs 0.2b (15.5%)

Compiler

Compiled 17834 to 12840 computations (28% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	31
1	62	31

end0.0ms (0%)

sample3.5s (21.9%)

Algorithm

1×

intervals

Results

850.0ms	7856×	body	128	valid
34.0ms	78×	body	1024	invalid
30.0ms	96×	body	512	invalid
30.0ms	279×	body	128	invalid
24.0ms	52×	body	1024	valid
20.0ms	71×	body	256	invalid
19.0ms	50×	body	512	valid
10.0ms	17×	body	2048	invalid
9.0ms	41×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 3011 to 2171 computations (27.9% saved)

Details

analyze2.4s (14.9%)

sample56.0ms (0.4%)

simplify53.0ms (0.3%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite177.0ms (1.1%)

series1.5s (9.2%)

simplify64.0ms (0.4%)

prune242.0ms (1.5%)

localize15.0ms (0.1%)

rewrite152.0ms (1%)

series1.4s (8.7%)

simplify82.0ms (0.5%)

prune198.0ms (1.2%)

localize29.0ms (0.2%)

rewrite259.0ms (1.6%)

series1.9s (11.9%)

simplify85.0ms (0.5%)

prune353.0ms (2.2%)

localize30.0ms (0.2%)

rewrite226.0ms (1.4%)

series1.9s (11.7%)

simplify81.0ms (0.5%)

prune264.0ms (1.7%)

regimes1.1s (6.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (21.9%)

Profiling