Details

analyze2.3s (23.6%)

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)

sample47.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
7.0ms	92×	body	128	nan
3.0ms	33×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify209.0ms (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: 14.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize15.0ms (0.2%)

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)))))
3.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
11.9b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1149`
38×	`add-sqr-sqrt_binary64_1133`
27×	`prod-exp_binary64_1160`
23×	`add-cbrt-cube_binary64_1147`
19×	`associate-r_binary64_1051` `div-exp_binary64_1162`
17×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
15×	`times-frac_binary64_1117`
13×	`associate-l_binary64_1052`
10×	`pow-exp_binary64_1179` `unswap-sqr_binary64_1079`
7×	`unpow-prod-down_binary64_1190` `cbrt-unprod_binary64_1144` `pow1_binary64_1172` `sqrt-prod_binary64_1127`
5×	`cbrt-undiv_binary64_1145`
4×	`sqrt-div_binary64_1128` `add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `unpow2_binary64_1176` `sqr-pow_binary64_1083` `associate-*r/_binary64_1053`
2×	`*-commutative_binary64_1042` `flip3--_binary64_1115` `pow-to-exp_binary64_1180` `flip--_binary64_1086`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110`

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))))

series1.1s (10.9%)

Counts

4 → 12

Calls

4 calls:

521.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
318.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
172.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
45.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5599	2845

prune388.0ms (4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Merged error: 5.8b

Counts

129 → 7

Compiler

Compiled 7257 to 5325 computations (26.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
4.7b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.3b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64_1149`
91×	`prod-exp_binary64_1160`
40×	`div-exp_binary64_1162`
30×	`add-cbrt-cube_binary64_1147`
25×	`pow-exp_binary64_1179`
23×	`associate-r_binary64_1051`
22×	`add-sqr-sqrt_binary64_1133`
15×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
11×	`times-frac_binary64_1117` `cbrt-unprod_binary64_1144`
8×	`1-exp_binary64_1155` `rec-exp_binary64_1161`
7×	`pow1_binary64_1172`
6×	`unpow-prod-down_binary64_1190` `cbrt-undiv_binary64_1145`
5×	`pow-to-exp_binary64_1180`
4×	`associate-l_binary64_1052` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `sqrt-prod_binary64_1127`
2×	`*-commutative_binary64_1042` `sqrt-div_binary64_1128` `unpow2_binary64_1176` `sqr-pow_binary64_1083`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `flip3--_binary64_1115` `associate-/l_binary64_1056` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `flip--_binary64_1086` `un-div-inv_binary64_1109` `associate-*r/_binary64_1053`

Counts

4 → 130

Calls

4 calls:

14.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
9.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))

series1.2s (12.6%)

Counts

4 → 12

Calls

4 calls:

593.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
409.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
171.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5297	2765

prune211.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	142	7	149

Merged error: 5.8b

Counts

149 → 7

Compiler

Compiled 3936 to 2676 computations (32% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.3b	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.9b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)

rewrite118.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

897×	`add-exp-log_binary64_1149`
537×	`prod-exp_binary64_1160`
487×	`add-cbrt-cube_binary64_1147`
277×	`cbrt-unprod_binary64_1144`
250×	`div-exp_binary64_1162`
131×	`cbrt-undiv_binary64_1145`
31×	`1-exp_binary64_1155` `rec-exp_binary64_1161`
16×	`associate-r_binary64_1051`
15×	`add-sqr-sqrt_binary64_1133` `pow1_binary64_1172`
13×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
12×	`times-frac_binary64_1117`
10×	`associate-*l/_binary64_1054`
7×	`pow-prod-down_binary64_1182`
6×	`associate-l_binary64_1052`
5×	`frac-times_binary64_1121`
4×	`div-inv_binary64_1108` `add-log-exp_binary64_1150`
3×	`associate-*r/_binary64_1053`
2×	`-commutative_binary64_1042` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l*_binary64_1056` `clear-num_binary64_1110`
1×	`unswap-sqr_binary64_1079` `un-div-inv_binary64_1109`

Counts

4 → 290

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
10.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series359.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
100.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
47.0ms	(/.f64 (.f64 M D) (.f64 2 d))
43.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5108	6589

prune465.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	301	8	309

Merged error: 5.1b

Counts

309 → 8

Compiler

Compiled 8284 to 5122 computations (38.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
9.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
26×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144`
21×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
19×	`add-sqr-sqrt_binary64_1133`
13×	`times-frac_binary64_1117` `-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146` `associate-r*_binary64_1051`
7×	`pow1_binary64_1172`
5×	`associate-l_binary64_1052`
4×	`div-inv_binary64_1108` `add-log-exp_binary64_1150`
3×	`sqrt-prod_binary64_1127`
2×	`sqrt-div_binary64_1128` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `unswap-sqr_binary64_1079` `clear-num_binary64_1110`
1×	`pow1/2_binary64_1191` `-commutative_binary64_1042` `associate-l/_binary64_1054` `rem-sqrt-square_binary64_1124` `frac-times_binary64_1121` `flip3--_binary64_1115` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `flip--_binary64_1086` `associate-*r/_binary64_1053`

Counts

4 → 109

Calls

4 calls:

17.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series499.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

296.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
117.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
45.0ms	(/.f64 (.f64 M D) (.f64 2 d))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5011	2149

prune155.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	120	9	129

Merged error: 5.1b

Counts

129 → 9

Compiler

Compiled 3650 to 1910 computations (47.7% saved)

regimes341.0ms (3.5%)

Compiler: Compiled 3339 to 2855 computations (14.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	194	94
1	194	94

end0.0ms (0%)

sample1.8s (18.3%)

Algorithm

1×

intervals

Results

646.0ms	8000×	body	128	valid
255.0ms	3084×	body	128	nan
114.0ms	1306×	body	128	invalid

Compiler

Compiled 336 to 274 computations (18.5% saved)

Details

analyze2.3s (23.6%)

sample47.0ms (0.5%)

simplify209.0ms (2.2%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite48.0ms (0.5%)

series1.1s (10.9%)

simplify56.0ms (0.6%)

prune388.0ms (4%)

localize15.0ms (0.2%)

rewrite55.0ms (0.6%)

series1.2s (12.6%)

simplify54.0ms (0.6%)

prune211.0ms (2.2%)

localize15.0ms (0.2%)

rewrite118.0ms (1.2%)

series359.0ms (3.7%)

simplify146.0ms (1.5%)

prune465.0ms (4.8%)

localize15.0ms (0.2%)

rewrite50.0ms (0.5%)

series499.0ms (5.2%)

simplify68.0ms (0.7%)

prune155.0ms (1.6%)

regimes341.0ms (3.5%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.8s (18.3%)

Profiling