Details

analyze486.0ms (7.9%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	40×	body	2048	valid
9.0ms	173×	body	128	valid
4.0ms	14×	body	4096	valid
3.0ms	18×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify370.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (277.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	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

Error

33.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.2b	(.f64 (.f64 3 a) c)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2146`
15×	`*-un-lft-identity_binary64_2124`
14×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`pow1_binary64_2185`
9×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `add-log-exp_binary64_2163` `times-frac_binary64_2130`
4×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076` `associate-r_binary64_2064`
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` `-commutative_binary64_2055` `associate-/r_binary64_2068` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `associate-l_binary64_2065` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 80

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series256.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
15.0ms	(.f64 (.f64 3 a) c)

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5038	1907

prune134.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

6.5b

Counts

93 → 9

Compiler

Compiled 2231 to 1343 computations (39.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(.f64 (.f64 3 a) c)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2146`
10×	`pow1_binary64_2185`
9×	`add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`add-cube-cbrt_binary64_2159`
4×	`cancel-sign-sub-inv_binary64_2090` `sqrt-prod_binary64_2140`
3×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `prod-exp_binary64_2173` `associate-r_binary64_2064` `cbrt-unprod_binary64_2157`
2×	`difference-of-squares_binary64_2093` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117`
1×	`distribute-lft-out--_binary64_2076` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `associate-l*_binary64_2065` `pow1/2_binary64_2204`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series173.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(.f64 (.f64 3 a) c)

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune78.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Error

6.5b

Counts

83 → 10

Compiler

Compiled 1742 to 1060 computations (39.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.4b	(/.f64 1/3 a)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2146`
17×	`*-un-lft-identity_binary64_2124`
15×	`add-cube-cbrt_binary64_2159`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`pow1_binary64_2185`
9×	`times-frac_binary64_2130`
6×	`add-log-exp_binary64_2163`
4×	`sqrt-prod_binary64_2140`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `prod-exp_binary64_2173` `associate-r_binary64_2064` `cbrt-unprod_binary64_2157`
2×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `sqrt-div_binary64_2141`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `distribute-lft-out--_binary64_2076` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `associate-l*_binary64_2065` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 77

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
3.0ms	(/.f64 1/3 a)

series152.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
16.0ms	(.f64 (.f64 3 a) c)
11.0ms	(/.f64 1/3 a)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4947	1222
1	4947	1222

prune95.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	90	9	99

Error

6.5b

Counts

99 → 9

Compiler

Compiled 1998 to 1212 computations (39.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.1b	(.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (/.f64 1/3 a))
9.5b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
24×	`*-un-lft-identity_binary64_2124`
22×	`add-sqr-sqrt_binary64_2146`
18×	`times-frac_binary64_2130`
17×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
16×	`add-cube-cbrt_binary64_2159`
13×	`cbrt-undiv_binary64_2158` `associate-r_binary64_2064` `div-exp_binary64_2175`
10×	`associate-l_binary64_2065`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
4×	`associate-/r/_binary64_2070` `distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068`
3×	`sqrt-prod_binary64_2140` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`unswap-sqr_binary64_2092` `sqrt-div_binary64_2141`
1×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `clear-num_binary64_2123` `flip3--_binary64_2128` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `associate-/l_binary64_2069` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `associate-l/_binary64_2067` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-r/_binary64_2066` `frac-times_binary64_2134` `frac-2neg_binary64_2135`

Counts

4 → 107

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (/.f64 1/3 a))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series474.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
148.0ms	(.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (/.f64 1/3 a))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5092	3382

prune151.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	118	10	128

Error

6.4b

Counts

128 → 10

Compiler

Compiled 3355 to 2026 computations (39.6% saved)

regimes1.1s (18.1%)

Accuracy

Total 1.1b remaining (16.7%)

Threshold costs 0b (0%)

Compiler

Compiled 5454 to 4194 computations (23.1% saved)

bsearch107.0ms (1.8%)

Steps

Iters	Range	Point
9	1.6162187021468506e+110	1.894050897151494e+115	3.432315266375116e+113
9	-5.337491136382482e-303	9.362734650379805e-307	-1.2677949885504426e-305
8	-5.675829841425222e+150	-1.975568661264478e+148	-1.7674460872703884e+149

Iters

Range

Point

1.6162187021468506e+110

1.894050897151494e+115

3.432315266375116e+113

-5.337491136382482e-303

9.362734650379805e-307

-1.2677949885504426e-305

-5.675829841425222e+150

-1.975568661264478e+148

-1.7674460872703884e+149

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	94
1	141	94

end0.0ms (0%)

sample2.0s (33.2%)

Algorithm

1×

intervals

Results

275.0ms	1121×	body	2048	valid
274.0ms	5196×	body	128	valid
136.0ms	716×	body	1024	valid
134.0ms	447×	body	4096	valid
52.0ms	366×	body	512	valid
35.0ms	670×	body	128	nan
22.0ms	381×	body	128	invalid
15.0ms	154×	body	256	valid

Compiler

Compiled 1061 to 808 computations (23.8% saved)

Details

analyze486.0ms (7.9%)

sample39.0ms (0.6%)

simplify370.0ms (6.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite37.0ms (0.6%)

series256.0ms (4.2%)

simplify59.0ms (1%)

prune134.0ms (2.2%)

localize10.0ms (0.2%)

rewrite27.0ms (0.4%)

series173.0ms (2.8%)

simplify63.0ms (1%)

prune78.0ms (1.3%)

localize11.0ms (0.2%)

rewrite27.0ms (0.4%)

series152.0ms (2.5%)

simplify65.0ms (1.1%)

prune95.0ms (1.5%)

localize14.0ms (0.2%)

rewrite54.0ms (0.9%)

series474.0ms (7.7%)

simplify79.0ms (1.3%)

prune151.0ms (2.5%)

regimes1.1s (18.1%)

bsearch107.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (33.2%)

Profiling