Details

analyze2.5s (25.6%)

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
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample46.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
7.0ms	83×	body	128	nan
3.0ms	38×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify214.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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: 14.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.6b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
12.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_805`
38×	`add-sqr-sqrt_binary64_789`
27×	`prod-exp_binary64_816`
23×	`add-cbrt-cube_binary64_803`
19×	`associate-r_binary64_707` `div-exp_binary64_818`
17×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
15×	`times-frac_binary64_773`
13×	`associate-l_binary64_708`
10×	`unswap-sqr_binary64_735` `pow-exp_binary64_835`
7×	`cbrt-unprod_binary64_800` `pow1_binary64_828` `unpow-prod-down_binary64_846` `sqrt-prod_binary64_783`
5×	`cbrt-undiv_binary64_801`
4×	`add-log-exp_binary64_806` `sqrt-div_binary64_784`
3×	`sqr-pow_binary64_739` `unpow2_binary64_832` `associate-*r/_binary64_709` `div-inv_binary64_764`
2×	`pow-to-exp_binary64_836` `*-commutative_binary64_698` `flip--_binary64_742` `flip3--_binary64_771`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r_binary64_711` `associate-/l_binary64_712` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `clear-num_binary64_766`

Counts

4 → 116

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (10.6%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
309.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
165.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
46.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5599	2845

prune436.0ms (4.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	11	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	11	129

Merged error: 6.9b

Counts

129 → 11

Compiler

Compiled 7720 to 5750 computations (25.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_805`
26×	`prod-exp_binary64_816`
23×	`add-cbrt-cube_binary64_803`
20×	`add-sqr-sqrt_binary64_789` `div-exp_binary64_818`
13×	`*-un-lft-identity_binary64_767`
10×	`associate-r_binary64_707` `pow-exp_binary64_835` `add-cube-cbrt_binary64_802`
6×	`cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `unpow-prod-down_binary64_846` `sqrt-prod_binary64_783`
5×	`pow1_binary64_828` `times-frac_binary64_773`
4×	`unswap-sqr_binary64_735` `associate-/r*_binary64_711` `add-log-exp_binary64_806`
3×	`associate-l_binary64_708` `div-inv_binary64_764`
2×	`frac-2neg_binary64_778` `pow-to-exp_binary64_836` `sqr-pow_binary64_739` `associate-/l*_binary64_712` `unpow2_binary64_832` `clear-num_binary64_766` `difference-of-squares_binary64_736` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `*-commutative_binary64_698` `distribute-lft-out--_binary64_719` `pow1/2_binary64_847` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771`

Counts

4 → 99

Calls

4 calls:

9.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
9.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.0s (10.3%)

Counts

4 → 12

Calls

4 calls:

580.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
195.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
183.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
43.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5310	2178

prune369.0ms (3.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 5.8b

Counts

122 → 13

Compiler

Compiled 6651 to 5111 computations (23.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
6.0b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
6.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite70.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
116×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
87×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
10×	`add-sqr-sqrt_binary64_789`
8×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
6×	`pow1_binary64_828` `times-frac_binary64_773`
5×	`associate-r_binary64_707` `associate-/r*_binary64_711`
4×	`add-log-exp_binary64_806` `associate-*r/_binary64_709` `div-inv_binary64_764`
3×	`associate-l_binary64_708` `frac-2neg_binary64_778` `associate-/l/_binary64_714` `associate-/l*_binary64_712` `clear-num_binary64_766`
1×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `-commutative_binary64_698` `associate-l/_binary64_710` `pow-prod-down_binary64_838`

Counts

4 → 153

Calls

4 calls:

20.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
10.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series377.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
83.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
46.0ms	(/.f64 (.f64 M D) (.f64 2 d))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4981	3130
1	4981	3130

prune335.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	168	10	178

Merged error: 5.3b

Counts

178 → 10

Compiler

Compiled 6374 to 4284 computations (32.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
6.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_805`
90×	`add-cbrt-cube_binary64_803`
41×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
32×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
8×	`add-sqr-sqrt_binary64_789`
6×	`pow1_binary64_828` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
5×	`associate-r_binary64_707`
4×	`times-frac_binary64_773` `add-log-exp_binary64_806` `div-inv_binary64_764`
3×	`associate-l_binary64_708` `frac-2neg_binary64_778` `associate-/r_binary64_711` `associate-/l_binary64_712` `clear-num_binary64_766`
2×	`associate-*r/_binary64_709`
1×	`unswap-sqr_binary64_735` `associate-/l/_binary64_714` `*-commutative_binary64_698` `pow-prod-down_binary64_838`

Counts

4 → 109

Calls

4 calls:

14.0ms	(/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series498.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
74.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
47.0ms	(/.f64 (.f64 M D) (.f64 2 d))
45.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5077	1994

prune196.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	121	10	131

Merged error: 5.3b

Counts

131 → 10

Compiler

Compiled 4788 to 2514 computations (47.5% saved)

regimes348.0ms (3.6%)

Compiler: Compiled 3477 to 3000 computations (13.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	99	48
1	99	48

end0.0ms (0%)

sample1.8s (18.3%)

Algorithm

1×

intervals

Results

638.0ms	8000×	body	128	valid
247.0ms	2956×	body	128	nan
113.0ms	1325×	body	128	invalid

Compiler

Compiled 331 to 280 computations (15.4% saved)

Details

analyze2.5s (25.6%)

sample46.0ms (0.5%)

simplify214.0ms (2.2%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite50.0ms (0.5%)

series1.0s (10.6%)

simplify59.0ms (0.6%)

prune436.0ms (4.5%)

localize14.0ms (0.1%)

rewrite42.0ms (0.4%)

series1.0s (10.3%)

simplify65.0ms (0.7%)

prune369.0ms (3.8%)

localize14.0ms (0.1%)

rewrite70.0ms (0.7%)

series377.0ms (3.9%)

simplify109.0ms (1.1%)

prune335.0ms (3.4%)

localize18.0ms (0.2%)

rewrite55.0ms (0.6%)

series498.0ms (5.1%)

simplify89.0ms (0.9%)

prune196.0ms (2%)

regimes348.0ms (3.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (18.3%)

Profiling