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)

sample95.0ms (1.6%)

Algorithm

1×

intervals

Results

39.0ms	112×	body	1024	valid
28.0ms	37×	body	2048	valid
15.0ms	47×	body	512	valid
3.0ms	18×	body	256	valid
3.0ms	42×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify169.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

Merged error: 36.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.8b	(sin.f64 (+.f64 x eps))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_2120` `add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099`
2×	`add-cube-cbrt_binary64_2131` `sin-sum_binary64_2229` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-exp-log_binary64_2134`
1×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `associate--l+_binary64_2038` `diff-sin_binary64_2246` `flip3--_binary64_2103` `flip--_binary64_2074` `distribute-lft-out--_binary64_2053` `diff-log_binary64_2188`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series97.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

67.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
30.0ms	(sin.f64 (+.f64 x eps))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4839	426
1	4839	426

prune30.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.4b

Counts

30 → 3

Compiler

Compiled 404 to 129 computations (68.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
4.7b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_2099`
18×	`add-sqr-sqrt_binary64_2120`
16×	`add-cube-cbrt_binary64_2131`
15×	`distribute-lft-out_binary64_2052` `times-frac_binary64_2105`
9×	`add-log-exp_binary64_2135`
8×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
6×	`pow1_binary64_2157`
5×	`associate-/l*_binary64_2046`
3×	`associate-l_binary64_2042` `sum-log_binary64_2187` `associate-/r_binary64_2045` `associate-r*_binary64_2041`
2×	`flip3-+_binary64_2102` `associate-/l/_binary64_2048` `flip-+_binary64_2073`
1×	`cbrt-undiv_binary64_2130` `*-commutative_binary64_2032` `div-exp_binary64_2147` `frac-2neg_binary64_2110` `prod-exp_binary64_2145` `sin-cos-mult_binary64_2252` `+-commutative_binary64_2031` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `clear-num_binary64_2098` `div-inv_binary64_2096` `cbrt-unprod_binary64_2129` `associate-+r+_binary64_2033`

Counts

4 → 78

Calls

4 calls:

9.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
8.0ms	(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))

series198.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
43.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
36.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
35.0ms	(+.f64 x (+.f64 x eps))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4861	1323
1	4861	1323

prune109.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 0.3b

Counts

93 → 8

Compiler

Compiled 1891 to 1289 computations (31.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
0.5b	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
4.6b	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2127`
24×	`add-sqr-sqrt_binary64_2120`
15×	`add-cube-cbrt_binary64_2131` `-un-lft-identity_binary64_2099` `associate-r*_binary64_2041`
10×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124`
7×	`pow1_binary64_2157` `add-exp-log_binary64_2134`
6×	`add-cbrt-cube_binary64_2132`
5×	`unswap-sqr_binary64_2067`
4×	`sqr-pow_binary64_2071` `add-log-exp_binary64_2135`
3×	`associate-l_binary64_2042` `unpow3_binary64_2162` `pow-unpow_binary64_2173` `cube-mult_binary64_2126`
1×	`pow1/3_binary64_2178` `pow-exp_binary64_2164` `*-commutative_binary64_2032` `pow-pow_binary64_2168` `rem-cube-cbrt_binary64_2121` `pow-to-exp_binary64_2165` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `rem-cbrt-cube_binary64_2122` `cos-sum_binary64_2230` `cbrt-unprod_binary64_2129`

Counts

4 → 86

Calls

4 calls:

10.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
5.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))
4.0ms	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))

series251.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
77.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
34.0ms	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
30.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4822	1676
1	4822	1676

prune137.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	98	8	106

Merged error: 0.1b

Counts

106 → 8

Compiler

Compiled 2192 to 1769 computations (19.3% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))) 3)))
0.2b	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
0.5b	(pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3)
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3))

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_2120` `cbrt-prod_binary64_2127`
18×	`associate-r_binary64_2041`
17×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
12×	`cube-div_binary64_2125`
10×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124`
9×	`pow1_binary64_2157` `add-exp-log_binary64_2134`
8×	`cbrt-div_binary64_2128` `add-cbrt-cube_binary64_2132`
7×	`sin-mult_binary64_2251`
6×	`cos-mult_binary64_2250` `associate-l_binary64_2042` `unswap-sqr_binary64_2067`
4×	`sqr-pow_binary64_2071` `associate-*r/_binary64_2043` `add-log-exp_binary64_2135`
3×	`frac-sub_binary64_2108` `unpow3_binary64_2162` `pow-unpow_binary64_2173` `flip3--_binary64_2103` `flip--_binary64_2074` `cube-mult_binary64_2126` `sub-div_binary64_2106`
2×	`*-commutative_binary64_2032` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `cbrt-unprod_binary64_2129`
1×	`pow1/3_binary64_2178` `pow-exp_binary64_2164` `pow-pow_binary64_2168` `rem-cube-cbrt_binary64_2121` `pow-to-exp_binary64_2165` `rem-cbrt-cube_binary64_2122`

Counts

4 → 109

Calls

4 calls:

16.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))) 3)))
9.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3))
9.0ms	(pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3)
6.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))

series771.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

310.0ms	(pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3)
225.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))) 3)))
160.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3))
76.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4971	3871
1	4971	3871

prune245.0ms (4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	115	14	129

Merged error: 0.0b

Counts

129 → 14

Compiler

Compiled 4146 to 2949 computations (28.9% saved)

regimes84.0ms (1.4%)

Compiler: Compiled 836 to 688 computations (17.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms (0%)

sample3.4s (55.6%)

Algorithm

1×

intervals

Results

1.3s	3442×	body	1024	valid
971.0ms	1235×	body	2048	valid
305.0ms	1392×	body	512	valid
93.0ms	1323×	body	128	valid
82.0ms	605×	body	256	valid
6.0ms	3×	body	4096	valid

Compiler

Compiled 459 to 380 computations (17.2% saved)

Details

analyze2.0ms (0%)

sample95.0ms (1.6%)

simplify169.0ms (2.8%)

prune2.0ms (0%)

localize11.0ms (0.2%)

rewrite14.0ms (0.2%)

series97.0ms (1.6%)

simplify76.0ms (1.2%)

prune30.0ms (0.5%)

localize13.0ms (0.2%)

rewrite37.0ms (0.6%)

series198.0ms (3.3%)

simplify77.0ms (1.3%)

prune109.0ms (1.8%)

localize14.0ms (0.2%)

rewrite30.0ms (0.5%)

series251.0ms (4.1%)

simplify77.0ms (1.3%)

prune137.0ms (2.3%)

localize23.0ms (0.4%)

rewrite58.0ms (1%)

series771.0ms (12.7%)

simplify79.0ms (1.3%)

prune245.0ms (4%)

regimes84.0ms (1.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (55.6%)

Profiling