Details

analyze449.0ms (6.6%)

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample44.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	36×	body	1280	valid
9.0ms	30×	body	2560	valid
9.0ms	160×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	19×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	11×	body	80	invalid
0.0ms	3×	body	160	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify424.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (409.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune4.0ms (0.1%)

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

Merged error: 34.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3207`
13×	`*-un-lft-identity_binary64_3222`
9×	`add-cbrt-cube_binary64_3194` `add-exp-log_binary64_3186`
8×	`add-log-exp_binary64_3187`
7×	`add-cube-cbrt_binary64_3193`
6×	`difference-of-squares_binary64_3251` `times-frac_binary64_3217` `sqrt-prod_binary64_3201` `associate-/l*_binary64_3286`
5×	`pow1_binary64_3164`
4×	`flip--_binary64_3248` `flip3--_binary64_3221`
3×	`distribute-lft-out--_binary64_3267`
2×	`sqrt-div_binary64_3202` `cbrt-undiv_binary64_3192` `associate-/l/_binary64_3288` `sub-neg_binary64_3226` `div-exp_binary64_3171` `diff-log_binary64_3133`
1×	`cbrt-unprod_binary64_3191` `sqrt-pow1_binary64_3203` `rem-sqrt-square_binary64_3210` `div-inv_binary64_3223` `associate-/r*_binary64_3285` `prod-exp_binary64_3169` `clear-num_binary64_3225` `frac-2neg_binary64_3215` `pow1/2_binary64_3154` `div-sub_binary64_3216`

Counts

4 → 70

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series533.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify124.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4988	1963
1	4988	1963

prune120.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 4.2b

Counts

83 → 8

Compiler

Compiled 2037 to 1221 computations (40.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite91.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_3217`
438×	`add-sqr-sqrt_binary64_3207`
363×	`*-un-lft-identity_binary64_3222`
289×	`add-cube-cbrt_binary64_3193`
74×	`difference-of-squares_binary64_3251`
71×	`associate-/r*_binary64_3285`
40×	`sqrt-prod_binary64_3201`
37×	`distribute-lft-out--_binary64_3267`
25×	`add-exp-log_binary64_3186`
17×	`div-inv_binary64_3223`
15×	`div-exp_binary64_3171`
13×	`add-cbrt-cube_binary64_3194`
8×	`add-log-exp_binary64_3187`
6×	`cbrt-undiv_binary64_3192` `pow1_binary64_3164`
5×	`associate-/r/_binary64_3287`
3×	`flip--_binary64_3248` `1-exp_binary64_3182` `rec-exp_binary64_3170` `flip3--_binary64_3221` `associate-/l*_binary64_3286`
2×	`sqrt-div_binary64_3202` `sub-neg_binary64_3226` `diff-log_binary64_3133`
1×	`pow-flip_binary64_3148` `sqrt-pow1_binary64_3203` `rem-sqrt-square_binary64_3210` `clear-num_binary64_3225` `frac-2neg_binary64_3215` `pow1/2_binary64_3154` `inv-pow_binary64_3140`

Counts

4 → 352

Calls

4 calls:

31.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series561.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
71.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify274.0ms (4%)

Algorithm

1×	egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4951	16279
1	4951	16279

prune735.0ms (10.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	363	1	364
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	363	9	372

Merged error: 4.2b

Counts

372 → 9

Compiler

Compiled 12658 to 7647 computations (39.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_3207`
17×	`*-un-lft-identity_binary64_3222`
13×	`add-cube-cbrt_binary64_3193` `associate-r_binary64_3281`
10×	`times-frac_binary64_3217`
9×	`add-cbrt-cube_binary64_3194` `add-exp-log_binary64_3186`
8×	`add-log-exp_binary64_3187`
7×	`pow1_binary64_3164`
6×	`associate-l_binary64_3282`
5×	`flip--_binary64_3248` `flip3--_binary64_3221` `sqrt-prod_binary64_3201`
4×	`difference-of-squares_binary64_3251`
2×	`cbrt-unprod_binary64_3191` `associate-*l/_binary64_3284` `sqrt-div_binary64_3202` `sub-neg_binary64_3226` `prod-exp_binary64_3169` `frac-times_binary64_3214` `diff-log_binary64_3133` `unswap-sqr_binary64_3250` `distribute-lft-out--_binary64_3267`
1×	`-commutative_binary64_3290` `sqrt-pow1_binary64_3203` `rem-sqrt-square_binary64_3210` `cbrt-undiv_binary64_3192` `associate-r/_binary64_3283` `div-inv_binary64_3223` `pow1/2_binary64_3154` `div-exp_binary64_3171` `pow-prod-down_binary64_3145`

Counts

4 → 79

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series521.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4957	2223
1	4957	2223

prune101.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Merged error: 4.2b

Counts

100 → 9

Compiler

Compiled 2245 to 1339 computations (40.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3207`
10×	`*-un-lft-identity_binary64_3222`
8×	`add-log-exp_binary64_3187` `sqrt-prod_binary64_3201`
6×	`add-cube-cbrt_binary64_3193` `pow1_binary64_3164`
4×	`sqrt-div_binary64_3202` `flip--_binary64_3248` `difference-of-squares_binary64_3251` `add-cbrt-cube_binary64_3194` `flip3--_binary64_3221` `add-exp-log_binary64_3186`
2×	`sqrt-pow1_binary64_3203` `rem-sqrt-square_binary64_3210` `sub-neg_binary64_3226` `pow1/2_binary64_3154` `diff-log_binary64_3133` `distribute-lft-out--_binary64_3267`

Counts

4 → 58

Calls

4 calls:

10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series492.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5010	1536

prune105.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 4.2b

Counts

79 → 9

Compiler

Compiled 2644 to 1563 computations (40.9% saved)

regimes246.0ms (3.6%)

Compiler: Compiled 396 to 342 computations (13.6% saved)

bsearch131.0ms (1.9%)

Steps

Iters	Range		Point
11	9.892368350376772e+35	4.583658751230337e+63	2.745365517689481e+58
10	2.35006783697244e-185	2.2169008179829164e-173	9.423055076460754e-180
9	-1.552896314026054e+55	-6.103621955125901e+49	-1.5313916223964738e+55

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	109	94
1	109	94

end0.0ms (0%)

sample1.5s (22%)

Algorithm

1×

intervals

Results

303.0ms	1031×	body	2560	valid
282.0ms	5119×	body	80	valid
222.0ms	897×	body	1280	valid
92.0ms	477×	body	640	valid
38.0ms	248×	body	320	valid
36.0ms	102×	body	5120	valid
36.0ms	717×	body	80	nan
20.0ms	372×	body	80	invalid
12.0ms	126×	body	160	valid

Compiler

Compiled 253 to 195 computations (22.9% saved)

Details

analyze449.0ms (6.6%)

sample44.0ms (0.6%)

simplify424.0ms (6.2%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series533.0ms (7.8%)

simplify124.0ms (1.8%)

prune120.0ms (1.8%)

localize12.0ms (0.2%)

rewrite91.0ms (1.3%)

series561.0ms (8.2%)

simplify274.0ms (4%)

prune735.0ms (10.8%)

localize11.0ms (0.2%)

rewrite42.0ms (0.6%)

series521.0ms (7.6%)

simplify97.0ms (1.4%)

prune101.0ms (1.5%)

localize13.0ms (0.2%)

rewrite35.0ms (0.5%)

series492.0ms (7.2%)

simplify98.0ms (1.4%)

prune105.0ms (1.5%)

regimes246.0ms (3.6%)

bsearch131.0ms (1.9%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample1.5s (22%)

Profiling