Details

analyze1.8s (19.4%)

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)

sample69.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
18.0ms	183×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4940	44
1	4940	44

prune8.0ms (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: 2.7b

Counts

2 → 1

Compiler

Compiled 120 to 104 computations (13.3% saved)

localize24.0ms (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)
1.6b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.8b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
30×	`associate--r+_binary64` `times-frac_binary64`
27×	`cancel-sign-sub-inv_binary64`
20×	`frac-sub_binary64`
15×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-*r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64`
5×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
4×	`associate-/l*_binary64` `div-inv_binary64` `sqrt-div_binary64`
3×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `*-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
9.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)

series643.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

389.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
129.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
105.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
20.0ms	(/.f64 2/3 t)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4978	3634
1	4978	3634

prune332.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	5	144

Merged error: 0.3b

Counts

144 → 5

Compiler

Compiled 7565 to 4212 computations (44.3% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.6b	(-.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))))
1.9b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

rewrite102.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64`
60×	`frac-sub_binary64`
49×	`add-cube-cbrt_binary64`
46×	`associate-r_binary64`
39×	`frac-times_binary64`
31×	`cbrt-prod_binary64`
30×	`associate--r+_binary64`
28×	`sqrt-prod_binary64`
27×	`associate-*r/_binary64` `cancel-sign-sub-inv_binary64`
25×	`flip3--_binary64` `add-exp-log_binary64` `flip--_binary64`
21×	`associate-*l/_binary64`
18×	`add-cbrt-cube_binary64`
15×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
10×	`unswap-sqr_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`div-inv_binary64`
3×	`sub-neg_binary64`
2×	`pow1/3_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `*-commutative_binary64`

Counts

4 → 193

Calls

4 calls:

28.0ms	(-.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))))
28.0ms	(.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)

series1.0s (10.8%)

Counts

4 → 12

Calls

4 calls:

476.0ms	(-.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))))
219.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
177.0ms	(cbrt.f64 t)
138.0ms	(cbrt.f64 t)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5009	8110

prune485.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	205	5	210

Merged error: 0.3b

Counts

210 → 5

Compiler

Compiled 10288 to 5055 computations (50.9% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2/3 t)
3.3b	(-.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))))))
3.6b	(log.f64 (exp.f64 (/.f64 2/3 t)))
5.8b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`log-pow_binary64`
39×	`times-frac_binary64` `exp-prod_binary64`
38×	`*-un-lft-identity_binary64` `associate--r+_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
35×	`cancel-sign-sub-inv_binary64`
19×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`frac-sub_binary64`
7×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`div-inv_binary64`
4×	`associate-r/_binary64` `associate-/l_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `flip-+_binary64`

Counts

4 → 133

Calls

4 calls:

23.0ms	(-.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)

series764.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

479.0ms	(-.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))))))
133.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
128.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
24.0ms	(/.f64 2/3 t)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	3121
1	4981	3121

prune251.0ms (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

Merged error: 0.3b

Counts

150 → 5

Compiler

Compiled 5878 to 3044 computations (48.2% saved)

localize16.0ms (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 x (+.f64 x (.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))))
0.1b	(*.f64 c (+.f64 a 5/6))
1.2b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`
12×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
9×	`times-frac_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-l_binary64` `unpow-prod-down_binary64`
5×	`unswap-sqr_binary64`
4×	`unpow-prod-up_binary64` `prod-exp_binary64` `associate--l+_binary64`
3×	`associate-/r_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `exp-lft-sqr_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 98

Calls

4 calls:

11.0ms	(.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))
5.0ms	(/.f64 x (+.f64 x (.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))))

series724.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

398.0ms	(/.f64 x (+.f64 x (.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))))
229.0ms	(.f64 y (pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (*.f64 a b))))
54.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
43.0ms	(*.f64 c (+.f64 a 5/6))

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4959	2502
1	4959	2502

prune239.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	110	5	115

Merged error: 0.0b

Counts

115 → 5

Compiler

Compiled 4790 to 3232 computations (32.5% saved)

regimes138.0ms (1.5%)

Compiler: Compiled 1076 to 1034 computations (3.9% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	219	56
1	219	56

end0.0ms (0%)

sample2.2s (23.1%)

Algorithm

1×

intervals

Results

838.0ms	8000×	body	128	valid
510.0ms	5050×	body	128	nan

Compiler

Compiled 324 to 267 computations (17.6% saved)

Details

analyze1.8s (19.4%)

sample69.0ms (0.7%)

simplify55.0ms (0.6%)

prune8.0ms (0.1%)

localize24.0ms (0.3%)

rewrite64.0ms (0.7%)

series643.0ms (6.8%)

simplify66.0ms (0.7%)

prune332.0ms (3.5%)

localize29.0ms (0.3%)

rewrite102.0ms (1.1%)

series1.0s (10.8%)

simplify90.0ms (1%)

prune485.0ms (5.2%)

localize24.0ms (0.3%)

rewrite64.0ms (0.7%)

series764.0ms (8.1%)

simplify77.0ms (0.8%)

prune251.0ms (2.7%)

localize16.0ms (0.2%)

rewrite41.0ms (0.4%)

series724.0ms (7.7%)

simplify87.0ms (0.9%)

prune239.0ms (2.5%)

regimes138.0ms (1.5%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.2s (23.1%)

Profiling