Details

analyze2.3s (24.4%)

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
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)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
9.0ms	107×	body	128	nan
3.0ms	39×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify202.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

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: 14.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
10.0b	(.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:

16.0ms	(.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)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (11.1%)

Counts

4 → 12

Calls

4 calls:

511.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
307.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
168.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5599	2845

prune304.0ms (3.3%)

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: 6.3b

Counts

129 → 7

Compiler

Compiled 5713 to 3991 computations (30.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.2b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1149`
26×	`prod-exp_binary64_1160`
23×	`add-cbrt-cube_binary64_1147`
20×	`add-sqr-sqrt_binary64_1133` `div-exp_binary64_1162`
13×	`*-un-lft-identity_binary64_1111`
10×	`add-cube-cbrt_binary64_1146` `associate-r_binary64_1051` `pow-exp_binary64_1179`
6×	`unpow-prod-down_binary64_1190` `cbrt-unprod_binary64_1144` `cbrt-undiv_binary64_1145` `sqrt-prod_binary64_1127`
5×	`times-frac_binary64_1117` `pow1_binary64_1172`
4×	`associate-/r*_binary64_1055` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `associate-l_binary64_1052`
2×	`sqrt-div_binary64_1128` `unpow2_binary64_1176` `frac-2neg_binary64_1122` `associate-/l*_binary64_1056` `difference-of-squares_binary64_1080` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180` `clear-num_binary64_1110`
1×	`pow1/2_binary64_1191` `*-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `flip3--_binary64_1115` `sqrt-pow1_binary64_1129` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086`

Counts

4 → 99

Calls

4 calls:

9.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
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 (11%)

Counts

4 → 12

Calls

4 calls:

597.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
208.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
175.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5310	2178

prune207.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Merged error: 6.1b

Counts

118 → 6

Compiler

Compiled 3770 to 2707 computations (28.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
17×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144`
13×	`add-sqr-sqrt_binary64_1133`
12×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
10×	`*-un-lft-identity_binary64_1111`
7×	`add-cube-cbrt_binary64_1146` `pow1_binary64_1172`
6×	`sqrt-prod_binary64_1127`
5×	`associate-l_binary64_1052`
4×	`add-log-exp_binary64_1150`
3×	`times-frac_binary64_1117` `div-inv_binary64_1108` `associate-r_binary64_1051`
2×	`sqrt-div_binary64_1128` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `difference-of-squares_binary64_1080` `clear-num_binary64_1110`
1×	`pow1/2_binary64_1191` `-commutative_binary64_1042` `associate-l/_binary64_1054` `rem-sqrt-square_binary64_1124` `flip3--_binary64_1115` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079` `sqrt-pow1_binary64_1129` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086`

Counts

4 → 89

Calls

4 calls:

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

series495.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

308.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)))
101.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4999	1766
1	4999	1766

prune127.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 6.1b

Counts

107 → 6

Compiler

Compiled 2920 to 1646 computations (43.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
4.2b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
5.7b	(*.f64 (/.f64 M 2) (/.f64 D d))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1149`
43×	`add-sqr-sqrt_binary64_1133`
26×	`prod-exp_binary64_1160` `*-un-lft-identity_binary64_1111`
25×	`times-frac_binary64_1117`
23×	`add-cbrt-cube_binary64_1147` `add-cube-cbrt_binary64_1146`
20×	`div-exp_binary64_1162`
19×	`associate-r_binary64_1051`
16×	`associate-l_binary64_1052`
10×	`pow-exp_binary64_1179`
7×	`unswap-sqr_binary64_1079` `pow1_binary64_1172`
6×	`cbrt-unprod_binary64_1144` `cbrt-undiv_binary64_1145` `sqrt-prod_binary64_1127`
4×	`add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `associate-/r*_binary64_1055`
2×	`*-commutative_binary64_1042` `sqrt-div_binary64_1128` `unpow2_binary64_1176` `difference-of-squares_binary64_1080` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180`
1×	`pow1/2_binary64_1191` `unpow-prod-down_binary64_1190` `associate-l/_binary64_1054` `rem-sqrt-square_binary64_1124` `frac-times_binary64_1121` `frac-2neg_binary64_1122` `flip3--_binary64_1115` `associate-/l_binary64_1056` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086` `associate-*r/_binary64_1053`

Counts

4 → 123

Calls

4 calls:

12.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
7.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
7.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))

series998.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

588.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
189.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
170.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
50.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5360	2553

prune159.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	6	141

Merged error: 6.1b

Counts

141 → 6

Compiler

Compiled 3185 to 1936 computations (39.2% saved)

regimes282.0ms (3%)

Compiler: Compiled 1487 to 1582 computations (-6.4% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	133	82
1	133	82

end0.0ms (0%)

sample1.7s (18%)

Algorithm

1×

intervals

Results

638.0ms	8000×	body	128	valid
252.0ms	3155×	body	128	nan
120.0ms	1347×	body	128	invalid

Compiler

Compiled 181 to 167 computations (7.7% saved)

Details

analyze2.3s (24.4%)

sample50.0ms (0.5%)

simplify202.0ms (2.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite48.0ms (0.5%)

series1.0s (11.1%)

simplify55.0ms (0.6%)

prune304.0ms (3.3%)

localize16.0ms (0.2%)

rewrite40.0ms (0.4%)

series1.0s (11%)

simplify62.0ms (0.7%)

prune207.0ms (2.2%)

localize14.0ms (0.1%)

rewrite41.0ms (0.4%)

series495.0ms (5.3%)

simplify73.0ms (0.8%)

prune127.0ms (1.4%)

localize14.0ms (0.1%)

rewrite47.0ms (0.5%)

series998.0ms (10.7%)

simplify48.0ms (0.5%)

prune159.0ms (1.7%)

regimes282.0ms (3%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.7s (18%)

Profiling