Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample76.0ms (1.2%)

Algorithm

1×

intervals

Results

37.0ms	111×	body	1024	valid
18.0ms	38×	body	2048	valid
8.0ms	42×	body	512	valid
3.0ms	22×	body	256	valid
3.0ms	43×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

38.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.8b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.5b	(sin.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
4×	`add-log-exp_binary64_2504`
3×	`add-cube-cbrt_binary64_2500` `cancel-sign-sub-inv_binary64_2431`
2×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `sin-sum_binary64_2598`
1×	`difference-of-squares_binary64_2434` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `diff-log_binary64_2557` `diff-sin_binary64_2615` `associate--l+_binary64_2402` `flip3--_binary64_2469`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series137.0ms (2.2%)

Counts

2 → 23

Calls

2 calls:

92.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
44.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 408 to 328 computations (19.6% saved)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5068	747

prune43.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

0.3b

Counts

50 → 4

Compiler

Compiled 663 to 260 computations (60.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_2465`
18×	`add-sqr-sqrt_binary64_2487`
16×	`add-cube-cbrt_binary64_2500`
15×	`times-frac_binary64_2471` `distribute-lft-out_binary64_2416`
9×	`add-log-exp_binary64_2504`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`pow1_binary64_2526`
5×	`associate-/l*_binary64_2410`
3×	`associate-/r_binary64_2409` `sum-log_binary64_2556` `associate-r_binary64_2405` `associate-l*_binary64_2406`
2×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439`
1×	`*-commutative_binary64_2396` `+-commutative_binary64_2395` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `unswap-sqr_binary64_2433` `sin-cos-mult_binary64_2621` `div-exp_binary64_2516` `div-inv_binary64_2462` `associate-+r+_binary64_2397` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`

Counts

4 → 78

Calls

4 calls:

8.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series350.0ms (5.7%)

Counts

4 → 46

Calls

4 calls:

143.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
84.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
62.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
61.0ms	(+.f64 x (+.f64 x eps))

Compiler

Compiled 1124 to 1028 computations (8.5% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4982	1888
1	4982	1888

prune135.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Error

0.3b

Counts

128 → 8

Compiler

Compiled 2522 to 1642 computations (34.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_2496`
7×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
3×	`pow1/3_binary64_2547`

Counts

4 → 40

Calls

4 calls:

9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series359.0ms (5.9%)

Counts

4 → 23

Calls

4 calls:

98.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
97.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
95.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
70.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1288 to 1110 computations (13.8% saved)

simplify122.0ms (2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4861	826
1	4861	826

prune112.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Error

0.3b

Counts

71 → 8

Compiler

Compiled 2153 to 1601 computations (25.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
0.2b	(*.f64 (cos.f64 x) (sin.f64 eps))
3.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_2487`
11×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504`
9×	`add-cube-cbrt_binary64_2500`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
6×	`associate-r_binary64_2405` `associate-l_binary64_2406`
3×	`cancel-sign-sub-inv_binary64_2431`
2×	`*-commutative_binary64_2396` `sum-log_binary64_2556` `unswap-sqr_binary64_2433` `diff-log_binary64_2557` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
1×	`flip3-+_binary64_2468` `difference-of-squares_binary64_2434` `+-commutative_binary64_2395` `flip--_binary64_2440` `flip-+_binary64_2439` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `sin-cos-mult_binary64_2621` `associate--l+_binary64_2402` `flip3--_binary64_2469`

Counts

4 → 66

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
6.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
5.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
4.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

series728.0ms (11.9%)

Counts

4 → 43

Calls

4 calls:

254.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
202.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
140.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
132.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

Compiler

Compiled 1138 to 859 computations (24.5% saved)

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5252	1962

prune91.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	101	8	109
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	103	14	117

Error

0.1b

Counts

117 → 14

Compiler

Compiled 2055 to 629 computations (69.4% saved)

regimes212.0ms (3.5%)

Accuracy

Total 0.3b remaining (71.4%)

Threshold costs 0.3b (71.4%)

Compiler

Compiled 2139 to 1517 computations (29.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	21
1	20	21

end0.0ms (0%)

sample3.3s (53.4%)

Algorithm

1×

intervals

Results

1.0s	3478×	body	1024	valid
840.0ms	1268×	body	2048	valid
271.0ms	1360×	body	512	valid
94.0ms	1327×	body	128	valid
75.0ms	562×	body	256	valid
6.0ms	5×	body	4096	valid

Compiler

Compiled 741 to 531 computations (28.3% saved)

Details

analyze2.0ms (0%)

sample76.0ms (1.2%)

simplify102.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite13.0ms (0.2%)

series137.0ms (2.2%)

simplify65.0ms (1.1%)

prune43.0ms (0.7%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series350.0ms (5.7%)

simplify79.0ms (1.3%)

prune135.0ms (2.2%)

localize15.0ms (0.2%)

rewrite19.0ms (0.3%)

series359.0ms (5.9%)

simplify122.0ms (2%)

prune112.0ms (1.8%)

localize14.0ms (0.2%)

rewrite29.0ms (0.5%)

series728.0ms (11.9%)

simplify81.0ms (1.3%)

prune91.0ms (1.5%)

regimes212.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (53.4%)

Profiling