Details

analyze875.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

sample130.0ms

Algorithm

intervals

Results

37.0ms	478×	body	80	nan
22.0ms	266×	body	80	invalid
21.0ms	256×	body	80	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4976	24
1	4976	24

prune22.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.2b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
0.3b	(*.f64 y (log.f64 z))
1.0b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
1.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_3769`
20×	`*-un-lft-identity_binary64_3784`
15×	`add-cube-cbrt_binary64_3755`
13×	`add-cbrt-cube_binary64_3756`
12×	`add-exp-log_binary64_3748` `log-prod_binary64_3702`
10×	`add-log-exp_binary64_3749` `associate-l_binary64_3844` `pow1_binary64_3730`
8×	`associate-r_binary64_3843`
6×	`distribute-lft-in_binary64_3826` `distribute-rgt-in_binary64_3827`
5×	`exp-prod_binary64_3738`
3×	`cbrt-unprod_binary64_3753` `times-frac_binary64_3779` `prod-exp_binary64_3735` `difference-of-squares_binary64_3813` `rem-exp-log_binary64_3746` `associate-/r*_binary64_3847`
2×	`-commutative_binary64_3852` `associate-l/_binary64_3846` `distribute-lft-out--_binary64_3829` `exp-diff_binary64_3745` `pow-prod-down_binary64_3711` `unswap-sqr_binary64_3812` `cbrt-undiv_binary64_3754` `log-pow_binary64_3705` `div-exp_binary64_3737` `diff-log_binary64_3700` `exp-sum_binary64_3743`
1×	`associate-/l/_binary64_3850` `difference-of-sqr-1_binary64_3814` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `div-inv_binary64_3785` `flip3--_binary64_3783` `associate-/l_binary64_3848` `associate--l+_binary64_3840` `flip--_binary64_3810` `associate-r/_binary64_3845` `sub-neg_binary64_3788` `sum-log_binary64_3699`

Counts

4 → 96

Calls

4 calls:

8.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
5.0ms	(*.f64 y (log.f64 z))
8.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
13.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series425.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
30.0ms	(*.f64 y (log.f64 z))
127.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
225.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

simplify72.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5146	1859

prune290.0ms

Filtered

79 candidates to 108 candidates (-36.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Merged error: 0.0b

Counts

110 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (/.f64 1 (.f64 a (exp.f64 (+.f64 (.f64 y (neg.f64 (log.f64 z))) (+.f64 b (.f64 t (neg.f64 (log.f64 a)))))))))
0.3b	(*.f64 y (neg.f64 (log.f64 z)))
0.3b	(*.f64 t (neg.f64 (log.f64 a)))
1.1b	(/.f64 (.f64 x (/.f64 1 (.f64 a (exp.f64 (+.f64 (.f64 y (neg.f64 (log.f64 z))) (+.f64 b (.f64 t (neg.f64 (log.f64 a))))))))) y)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log_binary64_3748`
32×	`associate-r_binary64_3843`
31×	`add-cbrt-cube_binary64_3756`
27×	`add-sqr-sqrt_binary64_3769`
21×	`*-un-lft-identity_binary64_3784` `add-cube-cbrt_binary64_3755`
16×	`prod-exp_binary64_3735`
14×	`pow1_binary64_3730`
12×	`distribute-neg-in_binary64_3822` `log-prod_binary64_3702`
10×	`cbrt-unprod_binary64_3753` `div-exp_binary64_3737`
9×	`associate-l_binary64_3844`
8×	`cbrt-undiv_binary64_3754` `distribute-lft-neg-in_binary64_3818` `distribute-rgt-neg-in_binary64_3819`
6×	`times-frac_binary64_3779` `distribute-lft-in_binary64_3826` `distribute-rgt-in_binary64_3827`
4×	`add-log-exp_binary64_3749` `log-pow_binary64_3705` `rec-exp_binary64_3736`
3×	`-commutative_binary64_3852` `associate-/r_binary64_3847` `pow-prod-down_binary64_3711` `unswap-sqr_binary64_3812` `distribute-rgt-neg-out_binary64_3821` `associate-*r/_binary64_3845`
2×	`un-div-inv_binary64_3786` `neg-mul-1_binary64_3791` `associate-/l/_binary64_3850` `div-inv_binary64_3785`
1×	`clear-num_binary64_3787` `frac-2neg_binary64_3777` `exp-diff_binary64_3745` `associate-/l*_binary64_3848` `associate-/r/_binary64_3849` `unsub-neg_binary64_3789` `associate-+r-_binary64_3837`

Counts

4 → 128

Calls

4 calls:

17.0ms	(.f64 x (/.f64 1 (.f64 a (exp.f64 (+.f64 (.f64 y (neg.f64 (log.f64 z))) (+.f64 b (.f64 t (neg.f64 (log.f64 a)))))))))
11.0ms	(*.f64 y (neg.f64 (log.f64 z)))
7.0ms	(*.f64 t (neg.f64 (log.f64 a)))
17.0ms	(/.f64 (.f64 x (/.f64 1 (.f64 a (exp.f64 (+.f64 (.f64 y (neg.f64 (log.f64 z))) (+.f64 b (.f64 t (neg.f64 (log.f64 a))))))))) y)

series559.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(.f64 x (/.f64 1 (.f64 a (exp.f64 (+.f64 (.f64 y (neg.f64 (log.f64 z))) (+.f64 b (.f64 t (neg.f64 (log.f64 a)))))))))
31.0ms	(*.f64 y (neg.f64 (log.f64 z)))
30.0ms	(*.f64 t (neg.f64 (log.f64 a)))
263.0ms	(/.f64 (.f64 x (/.f64 1 (.f64 a (exp.f64 (+.f64 (.f64 y (neg.f64 (log.f64 z))) (+.f64 b (.f64 t (neg.f64 (log.f64 a))))))))) y)

simplify95.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5227	2600

prune310.0ms

Filtered

88 candidates to 140 candidates (-59.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	141	4	145

Merged error: 0b

Counts

145 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z)))
0.3b	(*.f64 y (log.f64 z))
0.3b	(*.f64 t (log.f64 a))
0.9b	(/.f64 x (.f64 y (.f64 a (exp.f64 (-.f64 b (+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z))))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod_binary64_3702`
22×	`add-sqr-sqrt_binary64_3769`
18×	`*-un-lft-identity_binary64_3784` `add-cube-cbrt_binary64_3755`
17×	`add-cbrt-cube_binary64_3756`
16×	`add-exp-log_binary64_3748`
12×	`distribute-lft-in_binary64_3826` `distribute-rgt-in_binary64_3827`
10×	`pow1_binary64_3730`
8×	`associate-r_binary64_3843`
6×	`add-log-exp_binary64_3749` `associate-l_binary64_3844` `associate-+r+_binary64_3835` `associate-+l+_binary64_3836`
5×	`cbrt-unprod_binary64_3753` `prod-exp_binary64_3735`
3×	`times-frac_binary64_3779` `associate-/l*_binary64_3848` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737`
2×	`-commutative_binary64_3852` `pow-prod-down_binary64_3711` `unswap-sqr_binary64_3812` `log-pow_binary64_3705` `associate-r/_binary64_3845`
1×	`+-commutative_binary64_3851` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-/r*_binary64_3847` `exp-diff_binary64_3745` `div-inv_binary64_3785` `flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-/r/_binary64_3849` `sum-log_binary64_3699`

Counts

4 → 97

Calls

4 calls:

7.0ms	(+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z)))
5.0ms	(*.f64 y (log.f64 z))
8.0ms	(*.f64 t (log.f64 a))
13.0ms	(/.f64 x (.f64 y (.f64 a (exp.f64 (-.f64 b (+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z))))))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z)))
29.0ms	(*.f64 y (log.f64 z))
30.0ms	(*.f64 t (log.f64 a))
252.0ms	(/.f64 x (.f64 y (.f64 a (exp.f64 (-.f64 b (+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z))))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5053	1765

prune255.0ms

Filtered

80 candidates to 109 candidates (-36.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	110	3	113

Merged error: 0b

Counts

113 → 3

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z)))
0.3b	(*.f64 y (log.f64 z))
0.3b	(*.f64 t (log.f64 a))
7.7b	(/.f64 (/.f64 x y) (.f64 a (exp.f64 (-.f64 b (+.f64 (.f64 t (log.f64 a)) (*.f64 y (log.f64 z)))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_3769`
31×	`times-frac_binary64_3779`
30×	`*-un-lft-identity_binary64_3784` `add-cube-cbrt_binary64_3755`
24×	`log-prod_binary64_3702`
20×	`add-cbrt-cube_binary64_3756`
18×	`add-exp-log_binary64_3748`
13×	`associate-/l*_binary64_3848`
12×	`distribute-lft-in_binary64_3826` `distribute-rgt-in_binary64_3827`
10×	`pow1_binary64_3730`
8×	`associate-r_binary64_3843`
6×	`add-log-exp_binary64_3749` `associate-l_binary64_3844` `associate-+r+_binary64_3835` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737` `associate-+l+_binary64_3836`
4×	`cbrt-unprod_binary64_3753` `prod-exp_binary64_3735`
3×	`div-inv_binary64_3785`
2×	`*-commutative_binary64_3852` `pow-prod-down_binary64_3711` `unswap-sqr_binary64_3812` `log-pow_binary64_3705`
1×	`+-commutative_binary64_3851` `associate-/l/_binary64_3850` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-/r_binary64_3847` `exp-diff_binary64_3745` `flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-/r/_binary64_3849` `associate-r/_binary64_3845` `sum-log_binary64_3699`

Counts

4 → 120

Calls

4 calls:

6.0ms	(+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z)))
5.0ms	(*.f64 y (log.f64 z))
5.0ms	(*.f64 t (log.f64 a))
14.0ms	(/.f64 (/.f64 x y) (.f64 a (exp.f64 (-.f64 b (+.f64 (.f64 t (log.f64 a)) (*.f64 y (log.f64 z)))))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+.f64 (.f64 t (log.f64 a)) (.f64 y (log.f64 z)))
29.0ms	(*.f64 y (log.f64 z))
32.0ms	(*.f64 t (log.f64 a))
249.0ms	(/.f64 (/.f64 x y) (.f64 a (exp.f64 (-.f64 b (+.f64 (.f64 t (log.f64 a)) (*.f64 y (log.f64 z)))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5310	2455

prune290.0ms

Filtered

99 candidates to 132 candidates (-33.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	132	3	135

Merged error: 0b

Counts

135 → 3

regimes665.0ms

Accuracy

67.1% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 1.3b

bsearch286.0ms

Steps

Iters	Range	Point
9	4769101357733631/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152	738961397306651/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688	3.731887299802218e-81
10	-3343573933722397/194064761537588616893622436057812819407110752139587076392381504753256369085797110791359801103580809743810966337141384150771447505514351798930535909380147642400556872002606238193783160703949805603157874899214558593861605856727007232	-6024970209363407/3334007216439927137039925895360628898572379161157954080198128905882018618908816035760716100435777145371464955296716620222944400827059682540181678026165415023047578789757007279231539142955907012364482508067943300990845374018738230645581938688	-5.06359644977106e-218

Iters

Range

Point

4769101357733631/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152

738961397306651/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688

3.731887299802218e-81

-3343573933722397/194064761537588616893622436057812819407110752139587076392381504753256369085797110791359801103580809743810966337141384150771447505514351798930535909380147642400556872002606238193783160703949805603157874899214558593861605856727007232

-6024970209363407/3334007216439927137039925895360628898572379161157954080198128905882018618908816035760716100435777145371464955296716620222944400827059682540181678026165415023047578789757007279231539142955907012364482508067943300990845374018738230645581938688

-5.06359644977106e-218

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	92	70
1	92	70

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.0s	14555×	body	80	nan
668.0ms	8000×	body	80	valid
607.0ms	7359×	body	80	invalid

Details

analyze875.0ms

sample130.0ms

simplify91.0ms

prune22.0ms

localize25.0ms

rewrite35.0ms

series425.0ms

simplify72.0ms

prune290.0ms

localize30.0ms

rewrite56.0ms

series559.0ms

simplify95.0ms

prune310.0ms

localize24.0ms

rewrite37.0ms

series387.0ms

simplify54.0ms

prune255.0ms

localize32.0ms

rewrite33.0ms

series384.0ms

simplify65.0ms

prune290.0ms

regimes665.0ms

bsearch286.0ms

simplify4.0ms

end0.0ms

sample3.5s

Profiling