Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
7.0ms	256×	pre	80	true
5.0ms	23×	body	1280	valid
4.0ms	24×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	107	14
2	479	14
3	2315	14
4	5002	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.7b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.7b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
87×	`*-un-lft-identity`
46×	`fma-def`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`associate-/r/`
21×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-log-exp`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `frac-times` `sum-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`+-commutative` `frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-+l+`

Counts

4 → 178

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* 2.0 i))
20.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
35.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
15.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ alpha beta) (* 2.0 i))
229.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
272.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify107.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	724	2051
1	4101	1860
2	5001	1852

prune623.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.0b	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
2.7b	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt`
17×	`distribute-lft-out`
9×	`associate-/l*` `add-log-exp`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `fma-def` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l/`
3×	`sum-log`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `associate-+l+` `flip3--` `div-sub` `flip--` `fma-udef`

Counts

4 → 119

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* 2.0 i))
11.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
1.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

series409.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (+ alpha beta) (* 2.0 i))
71.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
241.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	523	1047
1	2277	969
2	5002	958

prune430.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
2.7b	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)
2.7b	(log (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
36×	`times-frac`
27×	`add-cube-cbrt`
16×	`distribute-lft-out`
9×	`associate-/l*`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log-prod` `associate-/r/` `log-pow` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`exp-prod` `flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`
1×	`flip3--` `div-sub` `rem-log-exp` `exp-sum` `flip--`

Counts

4 → 118

Calls

4 calls:

12.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
1.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)
2.0ms	(log (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
76.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
242.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)
243.0ms	(log (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	481	1287
1	1763	1170
2	5001	1157

prune500.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.5b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (sqrt (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0))))
2.5b	(log (sqrt (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0))))
2.7b	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)
2.7b	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`log-prod`
12×	`log-pow`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `sqrt-pow1` `sqrt-prod`
6×	`add-exp-log` `exp-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `rem-log-exp` `exp-sum`

Counts

4 → 66

Calls

4 calls:

3.0ms	(log (sqrt (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0))))
3.0ms	(log (sqrt (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0))))
1.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)
1.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

series1.3s

Counts

4 → 12

Calls

4 calls:

394.0ms	(log (sqrt (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0))))
391.0ms	(log (sqrt (exp (fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0))))
247.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)
242.0ms	(fma (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	182	1316
1	474	1168
2	1813	1158
3	5001	1136

prune393.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.5b

regimes256.0ms

Accuracy

9.1% (5.9b remaining)

Error of 11.7b against oracle of 5.8b and baseline of 12.3b

bsearch51.0ms

Steps

Iters	Range		Point
6	9.92406904354315e+79	9.709524947269395e+80	9.473490174268277e+80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	45	25
2	45	25

end0.0ms

sample998.0ms

Algorithm

intervals

Results

282.0ms	8000×	pre	80	true
264.0ms	6359×	body	80	valid
103.0ms	606×	body	640	valid
102.0ms	494×	body	1280	valid
41.0ms	338×	body	320	valid
17.0ms	203×	body	160	valid