Details

sample171.0ms

Algorithm

intervals

Results

72.0ms	1343×	body	80	nan
27.0ms	447×	body	80	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 112

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
8.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series373.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
109.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
163.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify67.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	580	1143
1	2309	897
2	5002	860

prune361.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 0.0b

Counts

126 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.1b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
74×	`add-sqr-sqrt`
72×	`associate-r`
58×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`unpow-prod-down`
41×	`add-exp-log`
24×	`div-exp`
19×	`fma-udef`
18×	`add-cbrt-cube`
17×	`exp-sum`
14×	`prod-exp`
8×	`pow-exp`
6×	`pow1` `div-inv` `unswap-sqr`
5×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 153

Calls

4 calls:

25.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
14.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series817.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
81.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
75.0ms	(fma (log (/ 1 a)) t b)
326.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify92.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	904	2177
1	4141	1915
2	5001	1905

prune598.0ms

Filtered

165 candidates to 124 candidates (75.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	165	5	170

Merged error: 0b

Counts

170 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
1.1b	(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `associate-r/` `div-exp` `prod-exp` `associate-/r` `cbrt-unprod` `fma-udef` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 58

Calls

4 calls:

1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
1.0ms	(fma (log (/ 1 a)) t b)
28.0ms	(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series569.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
77.0ms	(fma (log (/ 1 a)) t b)
78.0ms	(fma (log (/ 1 a)) t b)
331.0ms	(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify44.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	367	1015
1	1433	759
2	5001	754

prune325.0ms

Filtered

70 candidates to 58 candidates (82.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Merged error: 0b

Counts

75 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
4.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

3049×	`times-frac`
1216×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
241×	`fma-udef`
239×	`exp-sum`
144×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
39×	`add-exp-log`
37×	`div-exp`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `pow-exp`
5×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-2neg` `clear-num` `associate-/r/` `rem-exp-log` `associate-/l/`

Counts

4 → 1087

Calls

4 calls:

2.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
40.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

series748.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
81.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
76.0ms	(fma (log (/ 1 a)) t b)
505.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

simplify278.0ms

Algorithm

egg-herbie

Counts

1099 → 1099

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	28990

prune4.9s

Filtered

1099 candidates to 847 candidates (77.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1099	0	1099
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1099	5	1104

Merged error: 0b

Counts

1104 → 5

regimes261.0ms

Accuracy

83.7% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 1.2b

bsearch408.0ms

Steps

Iters	Range		Point
9	7.348486498325489e-127	2.1932446481510436e-117	4.717642965513083e-120
10	-1.3667098245908305e+37	-1.5465241855074316e+27	-8.226813781604714e+32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	24
1	33	24

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	45425×	body	80	nan
959.0ms	15222×	body	80	valid