Details

analyze779.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 51 to 41 computations (19.6% saved)

sample170.0ms (1%)

Algorithm

1×

intervals

Results

111.0ms	121×	body	1024	valid
22.0ms	36×	body	512	valid
17.0ms	76×	body	128	valid
9.0ms	23×	body	256	valid

Compiler

Compiled 101 to 83 computations (17.8% saved)

simplify129.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4940	77
1	4940	77

prune8.0ms (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: 0.3b

Counts

2 → 2

Compiler

Compiled 146 to 116 computations (20.5% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
2.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64_3169`
61×	`*-un-lft-identity_binary64_3147`
53×	`times-frac_binary64_3153`
43×	`associate-l_binary64_3088`
40×	`add-cube-cbrt_binary64_3182`
35×	`cancel-sign-sub-inv_binary64_3113`
20×	`sqrt-prod_binary64_3163`
17×	`difference-of-squares_binary64_3116`
14×	`distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
9×	`associate-r_binary64_3087` `distribute-lft-out--_binary64_3099`
8×	`pow1_binary64_3208` `add-log-exp_binary64_3186`
6×	`difference-of-sqr-1_binary64_3117`
4×	`unswap-sqr_binary64_3115` `sub-neg_binary64_3140`
3×	`flip--_binary64_3122` `flip3--_binary64_3151` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `div-inv_binary64_3144`
2×	`-commutative_binary64_3078` `pow-prod-down_binary64_3218` `diff-log_binary64_3239` `associate-r/_binary64_3089`
1×	`diff-cos_binary64_3298` `associate-*l/_binary64_3090` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198`

Counts

4 → 148

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
14.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

series417.0ms (2.4%)

Counts

4 → 25

Calls

4 calls:

197.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
139.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
81.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
0.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 2042 to 1698 computations (16.8% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4939	3022
1	4939	3022

prune700.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	162	11	173
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	163	12	175

Merged error: 0.1b

Counts

175 → 12

Compiler

Compiled 10459 to 7257 computations (30.6% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
0.3b	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
2.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite91.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-sqr-sqrt_binary64_3169`
74×	`*-un-lft-identity_binary64_3147`
72×	`times-frac_binary64_3153`
55×	`cancel-sign-sub-inv_binary64_3113`
53×	`add-cube-cbrt_binary64_3182`
44×	`associate-l_binary64_3088`
28×	`distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
17×	`difference-of-squares_binary64_3116`
16×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-prod_binary64_3163`
15×	`associate-r_binary64_3087`
13×	`pow1_binary64_3208`
10×	`associate-*r/_binary64_3089`
9×	`distribute-lft-out--_binary64_3099`
8×	`flip--_binary64_3122` `flip3--_binary64_3151`
6×	`difference-of-sqr-1_binary64_3117` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186`
5×	`pow-prod-down_binary64_3218` `sub-neg_binary64_3140` `div-inv_binary64_3144`
4×	`frac-times_binary64_3157` `unswap-sqr_binary64_3115`
3×	`-commutative_binary64_3078` `associate-l/_binary64_3090`
1×	`diff-cos_binary64_3298` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239`

Counts

4 → 185

Calls

4 calls:

24.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
14.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series901.0ms (5.1%)

Counts

4 → 35

Calls

4 calls:

378.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
301.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
141.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
81.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))

Compiler

Compiled 2966 to 2491 computations (16% saved)

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5030	6045

prune1.1s (6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	213	7	220
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	214	18	232

Merged error: 0.1b

Counts

232 → 18

Compiler

Compiled 14548 to 10107 computations (30.5% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 x) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 5) -1) 2))))
2.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite107.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_3169`
74×	`*-un-lft-identity_binary64_3147`
71×	`times-frac_binary64_3153`
55×	`cancel-sign-sub-inv_binary64_3113`
53×	`add-cube-cbrt_binary64_3182` `sqrt-prod_binary64_3163`
47×	`associate-l_binary64_3088`
28×	`distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
17×	`difference-of-squares_binary64_3116`
16×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
13×	`associate-r_binary64_3087` `associate-*r/_binary64_3089`
9×	`distribute-lft-out--_binary64_3099`
8×	`flip--_binary64_3122` `flip3--_binary64_3151`
7×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
6×	`difference-of-sqr-1_binary64_3117` `add-log-exp_binary64_3186`
5×	`frac-times_binary64_3157` `sub-neg_binary64_3140` `div-inv_binary64_3144`
4×	`sqrt-div_binary64_3164`
3×	`-commutative_binary64_3078` `associate-l/_binary64_3090`
2×	`unswap-sqr_binary64_3115`
1×	`diff-cos_binary64_3298` `diff-log_binary64_3239`

Counts

4 → 187

Calls

4 calls:

29.0ms	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 x) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 5) -1) 2))))
20.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series770.0ms (4.4%)

Counts

4 → 35

Calls

4 calls:

318.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
194.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
140.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
118.0ms	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 x) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 5) -1) 2))))

Compiler

Compiled 3455 to 2980 computations (13.7% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5082	6585

prune1.3s (7.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	223	17	240

Merged error: 0.1b

Counts

240 → 17

Compiler

Compiled 16429 to 11990 computations (27% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 x) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 5) -1) 2))))
0.7b	(pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3)
2.7b	(-.f64 (cos.f64 x) (cos.f64 y))
6.2b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3))

rewrite70.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_3169`
49×	`sqrt-prod_binary64_3163`
40×	`-un-lft-identity_binary64_3147` `associate-l*_binary64_3088`
33×	`times-frac_binary64_3153`
23×	`add-cube-cbrt_binary64_3182`
13×	`difference-of-squares_binary64_3116`
12×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
8×	`cbrt-prod_binary64_3178`
7×	`distribute-lft-out--_binary64_3099` `associate-*r/_binary64_3089`
6×	`difference-of-sqr-1_binary64_3117` `add-log-exp_binary64_3186`
4×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `cube-div_binary64_3176` `sqrt-div_binary64_3164`
3×	`flip--_binary64_3122` `cancel-sign-sub-inv_binary64_3113` `flip3--_binary64_3151` `pow-unpow_binary64_3224`
2×	`unpow-prod-down_binary64_3226` `cbrt-div_binary64_3179` `pow-exp_binary64_3215` `rem-cube-cbrt_binary64_3170` `cube-prod_binary64_3175` `sqr-pow_binary64_3119` `cube-mult_binary64_3177` `pow-pow_binary64_3219` `unpow3_binary64_3213`
1×	`rem-cbrt-cube_binary64_3171` `-commutative_binary64_3078` `diff-cos_binary64_3298` `frac-times_binary64_3157` `pow1/3_binary64_3229` `associate-l/_binary64_3090` `associate-r_binary64_3087` `pow-to-exp_binary64_3216` `sub-neg_binary64_3140` `diff-log_binary64_3239` `div-inv_binary64_3144`

Counts

4 → 118

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 x) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 5) -1) 2))))
11.0ms	(pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3)
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3))

series794.0ms (4.5%)

Counts

4 → 35

Calls

4 calls:

329.0ms	(pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3)
199.0ms	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3))
139.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
126.0ms	(.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2)) (.f64 (cos.f64 x) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 5) -1) 2))))

Compiler

Compiled 3652 to 3152 computations (13.7% saved)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4979	3473
1	4979	3473

prune766.0ms (4.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	152	18	170

Merged error: 0.1b

Counts

170 → 18

Compiler

Compiled 10653 to 7922 computations (25.6% saved)

regimes784.0ms (4.5%)

Compiler: Compiled 12266 to 10009 computations (18.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	103
1	92	103

end0.0ms (0%)

sample8.2s (46.8%)

Algorithm

1×

intervals

Results

3.2s	3519×	body	1024	valid
838.0ms	1352×	body	512	valid
503.0ms	2515×	body	128	valid
240.0ms	592×	body	256	valid
31.0ms	22×	body	2048	valid

Compiler

Compiled 4169 to 3404 computations (18.3% saved)

Details

analyze779.0ms (4.4%)

sample170.0ms (1%)

simplify129.0ms (0.7%)

prune8.0ms (0%)

localize35.0ms (0.2%)

rewrite69.0ms (0.4%)

series417.0ms (2.4%)

simplify79.0ms (0.4%)

prune700.0ms (4%)

localize32.0ms (0.2%)

rewrite91.0ms (0.5%)

series901.0ms (5.1%)

simplify71.0ms (0.4%)

prune1.1s (6%)

localize38.0ms (0.2%)

rewrite107.0ms (0.6%)

series770.0ms (4.4%)

simplify77.0ms (0.4%)

prune1.3s (7.4%)

localize40.0ms (0.2%)

rewrite70.0ms (0.4%)

series794.0ms (4.5%)

simplify82.0ms (0.5%)

prune766.0ms (4.4%)

regimes784.0ms (4.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.2s (46.8%)

Profiling