Details

analyze510.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample84.0ms (0.8%)

Algorithm

1×

intervals

Results

24.0ms	122×	body	256	valid
17.0ms	282×	pre	128	true
15.0ms	51×	body	512	valid
8.0ms	83×	body	128	valid
2.0ms	26×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify411.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 51.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite77.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_98`
13×	`*-un-lft-identity_binary64_77`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-log-exp_binary64_113`
7×	`add-cube-cbrt_binary64_109`
6×	`sqrt-prod_binary64_92` `times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
5×	`pow1_binary64_135`
4×	`flip--_binary64_52` `flip3--_binary64_81`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `sub-neg_binary64_70` `div-exp_binary64_125` `diff-log_binary64_166` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `prod-exp_binary64_123` `pow1/2_binary64_154` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 70

Calls

4 calls:

26.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
13.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series993.0ms (9%)

Counts

4 → 12

Calls

4 calls:

426.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
231.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
218.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
117.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify186.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune185.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.1b

Counts

83 → 3

Compiler

Compiled 1953 to 1159 computations (40.7% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.2b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite105.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
22×	`times-frac_binary64_83`
20×	`*-un-lft-identity_binary64_77`
17×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
13×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
11×	`associate-/l*_binary64_24`
10×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
8×	`add-log-exp_binary64_113`
6×	`associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1_binary64_135` `div-inv_binary64_74`
2×	`clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `flip3--_binary64_81` `diff-log_binary64_166` `associate-/l/_binary64_26` `sum-log_binary64_165`

Counts

4 → 98

Calls

4 calls:

30.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
26.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
17.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.6s (14.6%)

Counts

4 → 12

Calls

4 calls:

691.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
576.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
236.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify143.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune281.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 0.0b

Counts

113 → 7

Compiler

Compiled 3195 to 1969 computations (38.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_77`
15×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`times-frac_binary64_83`
8×	`add-log-exp_binary64_113`
6×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
5×	`pow1_binary64_135` `distribute-lft-out_binary64_30`
4×	`associate-/r*_binary64_23`
3×	`sqrt-prod_binary64_92` `associate-/l*_binary64_24`
2×	`flip-+_binary64_51` `sqrt-div_binary64_93` `flip3-+_binary64_80` `flip--_binary64_52` `associate-/r/_binary64_25` `flip3--_binary64_81`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `sub-neg_binary64_70` `+-commutative_binary64_9` `div-exp_binary64_125` `pow1/2_binary64_154` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

4 → 71

Calls

4 calls:

17.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series1.2s (11.1%)

Counts

4 → 12

Calls

4 calls:

622.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
244.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
225.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
139.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify159.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune206.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 0b

Counts

90 → 7

Compiler

Compiled 2260 to 1410 computations (37.6% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))

rewrite105.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-prod_binary64_92`
54×	`add-sqr-sqrt_binary64_98`
32×	`sqrt-pow1_binary64_94`
27×	`pow1_binary64_135`
24×	`sqrt-div_binary64_93` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
16×	`pow1/2_binary64_154`
15×	`swap-sqr_binary64_44`
9×	`associate-l_binary64_20` `times-frac_binary64_83` `pow-prod-up_binary64_144` `unswap-sqr_binary64_45` `associate-r_binary64_19`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `flip--_binary64_52` `flip3--_binary64_81`
5×	`pow-prod-down_binary64_145` `pow-sqr_binary64_50`
4×	`frac-times_binary64_87`
3×	`associate-/r_binary64_23` `associate-/l_binary64_24`
2×	`sub-neg_binary64_70` `associate-l/_binary64_22` `associate-r/_binary64_21` `associate-/r/_binary64_25` `diff-log_binary64_166`
1×	`rem-square-sqrt_binary64_89` `pow2_binary64_155` `flip-+_binary64_51` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `pow-plus_binary64_137` `flip3-+_binary64_80` `div-exp_binary64_125` `prod-exp_binary64_123` `*-commutative_binary64_10` `clear-num_binary64_76` `sqrt-unprod_binary64_96` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 134

Calls

4 calls:

37.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
10.0ms	(/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series1.1s (10.4%)

Counts

4 → 12

Calls

4 calls:

650.0ms	(/.f64 c (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
245.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
127.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
126.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4884	3430
1	4884	3430

prune384.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	146	7	153

Merged error: 0b

Counts

153 → 7

Compiler

Compiled 4657 to 2900 computations (37.7% saved)

regimes110.0ms (1%)

Compiler: Compiled 489 to 396 computations (19% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.8s (25.4%)

Algorithm

1×

intervals

Results

732.0ms	3856×	body	256	valid
509.0ms	8849×	pre	128	true
443.0ms	1536×	body	512	valid
253.0ms	2608×	body	128	valid
80.0ms	849×	body	128	nan

Compiler

Compiled 207 to 166 computations (19.8% saved)

Details

analyze510.0ms (4.6%)

sample84.0ms (0.8%)

simplify411.0ms (3.7%)

prune6.0ms (0.1%)

localize22.0ms (0.2%)

rewrite77.0ms (0.7%)

series993.0ms (9%)

simplify186.0ms (1.7%)

prune185.0ms (1.7%)

localize30.0ms (0.3%)

rewrite105.0ms (1%)

series1.6s (14.6%)

simplify143.0ms (1.3%)

prune281.0ms (2.5%)

localize25.0ms (0.2%)

rewrite61.0ms (0.6%)

series1.2s (11.1%)

simplify159.0ms (1.4%)

prune206.0ms (1.9%)

localize32.0ms (0.3%)

rewrite105.0ms (0.9%)

series1.1s (10.4%)

simplify127.0ms (1.1%)

prune384.0ms (3.5%)

regimes110.0ms (1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.8s (25.4%)

Profiling