Details

analyze480.0ms (5.1%)

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)

sample40.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	40×	body	2048	valid
9.0ms	169×	body	128	valid
4.0ms	19×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	16×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify396.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (301.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

32.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2146`
13×	`*-un-lft-identity_binary64_2124`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `times-frac_binary64_2130`
5×	`add-log-exp_binary64_2163`
4×	`pow1_binary64_2185`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076`
2×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `associate-/r*_binary64_2068` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

3 → 62

Calls

3 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series520.0ms (5.6%)

Counts

3 → 50

Calls

3 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
164.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
145.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1663 to 1387 computations (16.6% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5419	2348

prune147.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Error

5.2b

Counts

113 → 12

Compiler

Compiled 2470 to 1391 computations (43.7% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2146`
17×	`*-un-lft-identity_binary64_2124`
13×	`add-cube-cbrt_binary64_2159` `associate-r_binary64_2064`
10×	`times-frac_binary64_2130`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`pow1_binary64_2185` `associate-l_binary64_2065`
5×	`sqrt-prod_binary64_2140` `add-log-exp_binary64_2163`
4×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128`
3×	`cancel-sign-sub-inv_binary64_2090`
2×	`unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `sqrt-div_binary64_2141` `associate-*l/_binary64_2067` `prod-exp_binary64_2173` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `div-inv_binary64_2121` `div-exp_binary64_2175`

Counts

3 → 71

Calls

3 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series496.0ms (5.3%)

Counts

3 → 50

Calls

3 calls:

210.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
150.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1663 to 1387 computations (16.6% saved)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4956	2594
1	4956	2594

prune127.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

5.2b

Counts

133 → 10

Compiler

Compiled 2649 to 1493 computations (43.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))
0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite119.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

831×	`times-frac_binary64_2130`
550×	`add-sqr-sqrt_binary64_2146`
451×	`*-un-lft-identity_binary64_2124`
353×	`add-cube-cbrt_binary64_2159`
98×	`difference-of-squares_binary64_2093`
93×	`associate-/r*_binary64_2068`
52×	`sqrt-prod_binary64_2140`
49×	`distribute-lft-out--_binary64_2076`
30×	`add-exp-log_binary64_2162`
22×	`div-inv_binary64_2121`
18×	`add-cbrt-cube_binary64_2160` `div-exp_binary64_2175`
9×	`cbrt-undiv_binary64_2158`
6×	`associate-/r/_binary64_2070` `associate-/l*_binary64_2069` `pow1_binary64_2185` `add-log-exp_binary64_2163`
3×	`cancel-sign-sub-inv_binary64_2090` `1-exp_binary64_2168` `rec-exp_binary64_2174`
2×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `frac-2neg_binary64_2135`
1×	`sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `inv-pow_binary64_2209`

Counts

4 → 450

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
12.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series791.0ms (8.5%)

Counts

4 → 68

Calls

4 calls:

280.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2))
216.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
155.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
139.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2391 to 1991 computations (16.7% saved)

simplify210.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4988	21787
1	4988	21787

prune1.1s (11.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	515	3	518
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	518	10	528

Error

5.2b

Counts

528 → 10

Compiler

Compiled 17093 to 10255 computations (40% saved)

localize16.0ms (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) (sqrt.f64 1/2))
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.4b	(/.f64 (sqrt.f64 1/2) a)
20.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_2146`
28×	`*-un-lft-identity_binary64_2124`
24×	`add-cube-cbrt_binary64_2159`
21×	`sqrt-prod_binary64_2140`
18×	`times-frac_binary64_2130`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`pow1_binary64_2185`
6×	`associate-/l_binary64_2069` `add-log-exp_binary64_2163` `associate-l_binary64_2065` `associate-r*_binary64_2064`
4×	`difference-of-squares_binary64_2093`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `associate-/r*_binary64_2068`
2×	`unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `sqrt-div_binary64_2141` `associate-*l/_binary64_2067`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `*-commutative_binary64_2055` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 98

Calls

4 calls:

12.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (sqrt.f64 1/2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(/.f64 (sqrt.f64 1/2) a)

series563.0ms (6%)

Counts

4 → 53

Calls

4 calls:

224.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (sqrt.f64 1/2))
165.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
36.0ms	(/.f64 (sqrt.f64 1/2) a)

Compiler

Compiled 2270 to 1963 computations (13.5% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5014	2784

prune189.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	150	11	161

Error

5.2b

Counts

161 → 11

Compiler

Compiled 3724 to 2365 computations (36.5% saved)

regimes1.2s (13%)

Accuracy

Total 4.5b remaining (47.6%)

Threshold costs 0b (0%)

Compiler

Compiled 5908 to 4582 computations (22.4% saved)

bsearch58.0ms (0.6%)

Steps

Iters	Range		Point
9	9.424570629177468e-107	2.2753733693733163e-97	1.5261316372246074e-97
5	-2.3381053127520702e+145	-8.441216866363763e+144	-1.155604409696689e+145

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	48
1	90	48

end0.0ms (0%)

sample2.6s (27.6%)

Algorithm

1×

intervals

Results

312.0ms	1158×	body	2048	valid
289.0ms	5187×	body	128	valid
149.0ms	729×	body	1024	valid
118.0ms	366×	body	4096	valid
60.0ms	383×	body	512	valid
32.0ms	610×	body	128	nan
22.0ms	403×	body	128	invalid
20.0ms	177×	body	256	valid

Compiler

Compiled 1559 to 1203 computations (22.8% saved)

Details

analyze480.0ms (5.1%)

sample40.0ms (0.4%)

simplify396.0ms (4.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite29.0ms (0.3%)

series520.0ms (5.6%)

simplify67.0ms (0.7%)

prune147.0ms (1.6%)

localize14.0ms (0.1%)

rewrite33.0ms (0.4%)

series496.0ms (5.3%)

simplify66.0ms (0.7%)

prune127.0ms (1.4%)

localize12.0ms (0.1%)

rewrite119.0ms (1.3%)

series791.0ms (8.5%)

simplify210.0ms (2.2%)

prune1.1s (11.3%)

localize16.0ms (0.2%)

rewrite37.0ms (0.4%)

series563.0ms (6%)

simplify67.0ms (0.7%)

prune189.0ms (2%)

regimes1.2s (13%)

bsearch58.0ms (0.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (27.6%)

Profiling