Details

analyze1.7s (19.9%)

Algorithm

1×

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
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample66.0ms (0.8%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
16.0ms	171×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify141.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5053	44

prune5.0ms (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

5.8b

Counts

2 → 1

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b	(/.f64 2/3 t)
4.4b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.1b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_11353`
33×	`*-un-lft-identity_binary64_11331`
31×	`add-cube-cbrt_binary64_11366`
30×	`associate--r+_binary64_11267` `times-frac_binary64_11337`
27×	`cancel-sign-sub-inv_binary64_11297`
20×	`frac-sub_binary64_11340`
15×	`distribute-lft-in_binary64_11280` `distribute-rgt-in_binary64_11281`
13×	`add-exp-log_binary64_11369` `add-cbrt-cube_binary64_11367`
9×	`flip3--_binary64_11335` `flip--_binary64_11306`
8×	`frac-times_binary64_11341` `associate-*r/_binary64_11273`
7×	`associate-r_binary64_11271`
6×	`pow1_binary64_11392` `add-log-exp_binary64_11370` `associate-/r*_binary64_11275`
5×	`flip3-+_binary64_11334` `flip-+_binary64_11305` `sqrt-prod_binary64_11347`
4×	`associate-/l*_binary64_11276` `div-inv_binary64_11328` `sqrt-div_binary64_11348`
3×	`div-exp_binary64_11382` `sub-neg_binary64_11324` `cbrt-undiv_binary64_11365` `associate-l_binary64_11272`
2×	`associate--l+_binary64_11268` `cbrt-unprod_binary64_11364` `associate-/l/_binary64_11278` `unswap-sqr_binary64_11299` `frac-2neg_binary64_11342` `associate-*l/_binary64_11274` `prod-exp_binary64_11380` `clear-num_binary64_11330`
1×	`*-commutative_binary64_11262` `distribute-lft-out_binary64_11282` `diff-log_binary64_11423` `pow-prod-down_binary64_11402`

Counts

4 → 131

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
7.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)

series317.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
64.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
51.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
10.0ms	(/.f64 2/3 t)

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4945	3630
1	4945	3630

prune247.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	4	144

Error

1.5b

Counts

144 → 4

Compiler

Compiled 5812 to 2896 computations (50.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
2.3b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
4.4b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))

rewrite95.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64_11353`
76×	`times-frac_binary64_11337`
61×	`*-un-lft-identity_binary64_11331`
60×	`frac-sub_binary64_11340`
49×	`add-cube-cbrt_binary64_11366`
46×	`associate-r_binary64_11271`
39×	`frac-times_binary64_11341`
31×	`cbrt-prod_binary64_11362`
30×	`associate--r+_binary64_11267`
28×	`sqrt-prod_binary64_11347`
27×	`cancel-sign-sub-inv_binary64_11297` `associate-*r/_binary64_11273`
25×	`add-exp-log_binary64_11369` `flip3--_binary64_11335` `flip--_binary64_11306`
21×	`associate-*l/_binary64_11274`
18×	`add-cbrt-cube_binary64_11367`
15×	`distribute-lft-in_binary64_11280` `distribute-rgt-in_binary64_11281`
10×	`unswap-sqr_binary64_11299`
9×	`flip3-+_binary64_11334` `flip-+_binary64_11305`
8×	`cbrt-unprod_binary64_11364` `prod-exp_binary64_11380`
7×	`div-exp_binary64_11382` `cbrt-undiv_binary64_11365` `associate-l_binary64_11272`
6×	`pow1_binary64_11392` `add-log-exp_binary64_11370` `distribute-lft-out_binary64_11282`
4×	`div-inv_binary64_11328`
3×	`sub-neg_binary64_11324`
2×	`associate--l+_binary64_11268` `pow1/3_binary64_11413`
1×	`*-commutative_binary64_11262` `diff-log_binary64_11423` `pow-prod-down_binary64_11402`

Counts

4 → 193

Calls

4 calls:

25.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
25.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series542.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
129.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
89.0ms	(cbrt.f64 t)
82.0ms	(cbrt.f64 t)

simplify96.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5061	8091

prune510.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	204	5	209

Error

1.0b

Counts

209 → 5

Compiler

Compiled 10272 to 5071 computations (50.6% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2/3 t)
2.0b	(log.f64 (exp.f64 (/.f64 2/3 t)))
5.1b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
6.0b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`log-pow_binary64_11420`
39×	`times-frac_binary64_11337` `exp-prod_binary64_11383`
38×	`associate--r+_binary64_11267` `*-un-lft-identity_binary64_11331` `add-cube-cbrt_binary64_11366` `add-sqr-sqrt_binary64_11353`
35×	`cancel-sign-sub-inv_binary64_11297`
19×	`distribute-lft-in_binary64_11280` `distribute-rgt-in_binary64_11281`
11×	`add-exp-log_binary64_11369` `add-cbrt-cube_binary64_11367`
8×	`frac-sub_binary64_11340`
7×	`pow1_binary64_11392` `flip3--_binary64_11335` `flip--_binary64_11306`
6×	`add-log-exp_binary64_11370` `associate-/r*_binary64_11275`
5×	`div-inv_binary64_11328`
4×	`associate-/l_binary64_11276` `frac-times_binary64_11341` `associate-r/_binary64_11273`
3×	`log-prod_binary64_11417` `div-exp_binary64_11382` `sub-neg_binary64_11324` `cbrt-undiv_binary64_11365`
2×	`associate--l+_binary64_11268` `associate-/l/_binary64_11278` `frac-2neg_binary64_11342` `associate-*l/_binary64_11274` `sqrt-div_binary64_11348` `clear-num_binary64_11330`
1×	`cbrt-unprod_binary64_11364` `rem-log-exp_binary64_11372` `prod-exp_binary64_11380` `diff-log_binary64_11423` `flip3-+_binary64_11334` `flip-+_binary64_11305`

Counts

4 → 133

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
3.0ms	(/.f64 2/3 t)

series390.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
76.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
64.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
10.0ms	(/.f64 2/3 t)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5107	3121

prune233.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	145	5	150

Error

1.0b

Counts

150 → 5

Compiler

Compiled 5873 to 3046 computations (48.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
0.0b	(+.f64 a 5/6)
0.2b	(*.f64 c (+.f64 a 5/6))
0.7b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_11353`
16×	`associate-r_binary64_11271`
15×	`*-un-lft-identity_binary64_11331`
10×	`add-exp-log_binary64_11369`
9×	`add-cube-cbrt_binary64_11366`
8×	`add-log-exp_binary64_11370` `add-cbrt-cube_binary64_11367`
6×	`pow1_binary64_11392` `associate-l_binary64_11272` `unpow-prod-down_binary64_11410`
5×	`unswap-sqr_binary64_11299`
4×	`associate--l+_binary64_11268` `unpow-prod-up_binary64_11409` `prod-exp_binary64_11380`
3×	`distribute-lft-in_binary64_11280` `distribute-rgt-in_binary64_11281` `associate-*r/_binary64_11273`
2×	`*-commutative_binary64_11262` `cbrt-unprod_binary64_11364` `sub-neg_binary64_11324` `cancel-sign-sub-inv_binary64_11297` `distribute-lft-out_binary64_11282` `flip3-+_binary64_11334` `flip-+_binary64_11305` `exp-lft-sqr_binary64_11386` `sqr-pow_binary64_11303`
1×	`+-commutative_binary64_11261` `sum-log_binary64_11422` `pow-sub_binary64_11407` `flip3--_binary64_11335` `diff-log_binary64_11423` `pow-prod-down_binary64_11402` `pow-to-exp_binary64_11400` `pow-exp_binary64_11399` `flip--_binary64_11306`

Counts

4 → 81

Calls

4 calls:

8.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
7.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
7.0ms	(*.f64 c (+.f64 a 5/6))
3.0ms	(+.f64 a 5/6)

series182.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
30.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
21.0ms	(*.f64 c (+.f64 a 5/6))
10.0ms	(+.f64 a 5/6)

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4916	1421
1	4916	1421

prune110.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	93	5	98

Error

0.5b

Counts

98 → 5

Compiler

Compiled 2179 to 1269 computations (41.8% saved)

regimes883.0ms (10.1%)

Accuracy

Total 1.7b remaining (80.6%)

Threshold costs 0b (0%)

Compiler

Compiled 12622 to 9968 computations (21% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 23 computations (4.2% saved)

simplify39.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	942	165
1	942	165

end0.0ms (0%)

sample2.7s (30.7%)

Algorithm

1×

intervals

Results

792.0ms	8000×	body	128	valid
506.0ms	5078×	body	128	nan

Compiler

Compiled 1212 to 930 computations (23.3% saved)

Details

analyze1.7s (19.9%)

sample66.0ms (0.8%)

simplify141.0ms (1.6%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

rewrite57.0ms (0.6%)

series317.0ms (3.6%)

simplify101.0ms (1.2%)

prune247.0ms (2.8%)

localize29.0ms (0.3%)

rewrite95.0ms (1.1%)

series542.0ms (6.2%)

simplify96.0ms (1.1%)

prune510.0ms (5.8%)

localize25.0ms (0.3%)

rewrite56.0ms (0.6%)

series390.0ms (4.4%)

simplify67.0ms (0.8%)

prune233.0ms (2.7%)

localize14.0ms (0.2%)

rewrite33.0ms (0.4%)

series182.0ms (2.1%)

simplify71.0ms (0.8%)

prune110.0ms (1.3%)

regimes883.0ms (10.1%)

bsearch3.0ms (0%)

simplify39.0ms (0.4%)

end0.0ms (0%)

sample2.7s (30.7%)

Profiling