Details

sample180.0ms

Algorithm

intervals

Results

75.0ms	1501×	body	80	nan
30.0ms	479×	body	80	valid

simplify51.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.2b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite129.0ms

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:

11.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
32.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
79.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series411.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (- t 1.0) (log a))
62.0ms	(* y (log z))
113.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
173.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify73.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (60.0ms)

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

prune418.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

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)
1.2b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
16×	`div-exp`
13×	`add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-exp` `log1p-expm1-u`
3×	`exp-prod` `times-frac` `associate-/r*` `fma-udef`
2×	`cbrt-unprod`
1×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `exp-sum` `clear-num` `div-inv` `rem-exp-log` `associate-/l/` `associate-/l`

Counts

4 → 65

Calls

4 calls:

1.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
16.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series579.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
83.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
80.0ms	(fma (log (/ 1 a)) t b)
328.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	451	876
1	1703	729
2	5001	720

prune346.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)
1.2b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-exp-log`
60×	`prod-exp`
48×	`div-exp`
25×	`add-cbrt-cube`
16×	`pow-exp`
13×	`associate-r`
12×	`add-sqr-sqrt` `add-cube-cbrt` `rec-exp` `*-un-lft-identity` `1-exp`
10×	`cbrt-unprod`
9×	`pow1` `times-frac`
5×	`cbrt-undiv` `add-log-exp`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u`
3×	`exp-prod` `associate-*r/` `pow-prod-down` `fma-udef`
1×	`frac-times` `associate-l` `exp-sum` `associate-l/` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 102

Calls

4 calls:

1.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
47.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

series592.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
84.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
72.0ms	(fma (log (/ 1 a)) t b)
345.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

simplify69.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	674	1480
1	2631	1239
2	5001	1160

prune384.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 y))
0.6b	(cbrt (/ 1 y))
0.6b	(cbrt (/ 1 y))
0.9b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (* (cbrt (/ 1 y)) (cbrt (/ 1 y))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
39×	`cbrt-prod`
38×	`prod-exp`
27×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
16×	`pow1` `div-exp`
13×	`cbrt-unprod`
11×	`cbrt-div`
9×	`associate-*r/`
8×	`pow-prod-down` `pow-exp`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-*l/` `div-inv`
2×	`cbrt-undiv` `pow-to-exp` `rec-exp` `1-exp`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 117

Calls

4 calls:

1.0ms	(cbrt (/ 1 y))
1.0ms	(cbrt (/ 1 y))
2.0ms	(cbrt (/ 1 y))
60.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (* (cbrt (/ 1 y)) (cbrt (/ 1 y))))

series1.0s

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (/ 1 y))
179.0ms	(cbrt (/ 1 y))
185.0ms	(cbrt (/ 1 y))
493.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (* (cbrt (/ 1 y)) (cbrt (/ 1 y))))

simplify68.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	563	1447
1	2190	1183
2	5002	1101

prune555.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes346.0ms

Accuracy

92.8% (0.1b remaining)

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

bsearch101.0ms

Steps

Iters	Range		Point
7	1.9235068891934086e-20	9.276445317274726e-19	4.546468324989515e-20

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	25
1	30	25

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	45275×	body	80	nan
929.0ms	14960×	body	80	valid